Monitoring a system during low-pressure processes

ABSTRACT

A method of monitoring a processing system in real-time using low-pressure based modeling techniques that include processing one or more of wafers in a processing chamber; determining a measured dynamic process response for a rate of change for a process parameter; executing a real-time dynamic model to generate a predicted dynamic process response; determining a dynamic estimation error using a difference between the predicted dynamic process response and the expected process response; and comparing the dynamic estimation error to operational limits.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to co-pending U.S. Patent Application No.______ (Attorney Docket No. TPS-030), entitled “MONITORING A MONOLAYERDEPOSITION (MLD) SYSTEM USING A BUILT-IN SELF TEST (BIST) TABLE”, filedon even date herewith, co-pending U.S. Patent Application No. ______(Attorney Docket No. TPS-031), entitled“METHOD FOR CREATING A BUILT-INSELF TEST (BIST) TABLE FOR MONITORING A MONOLAYER DEPOSITION (MLD)SYSTEM” filed on even date herewith, and co-pending U.S. PatentApplication No. ______ (Attorney Docket No. TPS-032), entitled“MONITORING A SINGLE-WAFER PROCESSING SYSTEM”, filed on even dateherewith. The entire contents of these applications are hereinincorporated by reference in their entirety.

FIELD OF THE INVENTION

This invention relates to methods for monitoring a system to detect,diagnose, and predict fault conditions for a system employed inlow-pressure semiconductor processing.

BACKGROUND OF THE INVENTION

Several processes in semiconductor manufacturing involve processingwafers at low-pressure. In a typical such process, the process chamberis brought to a reduced pressure; subsequently certain process gases areintroduced into the chamber to create desired process conditions.

For illustration purpose, we describe one such process in some detail.Several methods have been developed for creating thin films on wafersused in manufacturing semiconductor devices. Among the more establishedtechniques is Chemical Vapor Deposition (CVD). Atomic Layer Deposition(ALD), a variant of CVD, is a relatively newer technology now emergingas a potentially superior method of achieving highly uniform, conformalfilm deposition.

ALD has demonstrated an outstanding ability to maintain ultra-uniformthin deposition layers over complex topology. This is at least partiallytrue because ALD is not as flux dependent as is CVD. Thisflux-independent nature of ALD allows processing at lower temperaturesthan with conventional CVD methods.

The technique of ALD is based on the principle of the formation of asaturated monolayer of reactive precursor molecules by chemisorption. Atypical ALD process consists of injecting a precursor R_(A) for a periodof time until a saturated monolayer is formed on the wafer. Then, theprecursor R_(A) is purged from the chamber using an inert gas, GI. Thisis followed by injecting precursor R_(B) into the chamber, also for aperiod of time, thus forming the layer AB on the wafer. Then, theprecursor R_(B) is purged from the chamber. This process of introducingR_(A), purging the reactor, introducing R_(B), and purging the reactorcan be repeated a number of times to achieve an AB film of a desiredthickness.

This process is also illustrative of the types of issues encountered insuch low-pressure processing. For example:

1) Film quality and composition can be greatly impacted in the casewhere the flow rates of the Reactants R_(A) and R_(B) fail to be asdesired in the recipe. For example, if the MFC corresponding to thereactant fails to perform as desired to deliver the recipe setpoint flowrate value, the film quality can be affected.

2) In-situ measurements providing details of wafer condition, such aswhen saturation of a precursor monolayer is completed on the wafer(s),are not available; this hinders the ability to control and optimizeprocessing conditions so as to achieve optimal performance andthroughput.

SUMMARY OF THE INVENTION

The present invention provides a method and apparatus for indicatingdegraded performance of the reactant flow rates in low-pressureprocesses. The invention provides a method of monitoring a processingsystem that includes performing a process on one or more wafers in aprocessing chamber having a reduced pressure; and monitoring the processusing a process model, the process model being created using a set ofnonlinear differential equations {dot over (x)}₁ and an output equationy₁, as follows:{dot over (x)} ₁=ƒ(x ₁ ,p ₁ , u ₁)+w ₁y ₁ =g(x ₁ ,p ₁ , u ₁)+v ₁wherein x₁, p₁, and u₁ are first process parameters in which the vectorx₁ comprises a state vector, the vector p₁ comprises one or moremodeling parameters, the vector u₁ comprises one or more inputs appliedto the process, w₁ is a first additive white noise value having a zeromean, and v₁ is a second additive white noise value having a zero mean.The method includes determining a first process model for the firstprocess that relates a first rate of change for at least one parameterof a first set of first process parameters to a second set of firstprocess parameters as and/or after a first parameter in the second setis changed from a first value to a second value, wherein the second setdoes not include the at least one parameter of the first set;determining a first measured rate of change for the at least oneparameter of the first set, wherein the first measured rate of change isdetermined in real time as and/or after the first parameter in thesecond set is changed from the first value to the second value;executing a first inverse process model for the first process thatrelates the first measured rate of change to a value for a secondparameter in the second set to obtain a predicted value for the secondparameter in the second set; and calculating a first dynamic estimationerror for the first process. The method further includes comparing thefirst dynamic estimation error for the first process to a firstoperational limit established for the first process; continuing thefirst process when the first dynamic estimation error is within thefirst operational limit; and examining the first process when the firstdynamic estimation error is not within the first operational limit.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the invention and many of the attendantadvantages thereof will become readily apparent with reference to thefollowing detailed description, particularly when considered inconjunction with the accompanying drawings, in which:

FIG. 1 is an isometric view of a processing system in accordance withembodiments of the invention;

FIG. 2 is a partial cut-away schematic view of a portion of a processingsystem in accordance with embodiments of the invention;

FIG. 3 illustrates a simplified block diagram of a processing system inaccordance with embodiments of the invention;

FIG. 4 shows the chamber pressure transient behavior for a firstpressure setpoint change in accordance with embodiments of theinvention;

FIG. 5 shows the chamber pressure transient behavior for a secondpressure setpoint change in accordance with embodiments of theinvention;

FIG. 6 shows the chamber pressure transient behavior for a thirdpressure setpoint change in accordance with embodiments of theinvention;

FIG. 7 shows rise rate as a function of gas flow rate for the three stepresponse test cases in accordance with embodiments of the invention;

FIG. 8 shows chamber pressure as a function of flow rates at variousvalve angles in accordance with embodiments of the invention;

FIG. 9 illustrates a schematic representation of an embodiment of thedynamic model characterizing one or more of the responses of aprocessing system in accordance with an embodiment of the invention;

FIG. 10 illustrates a simplified schematic drawing for a processingsystem in accordance with embodiments of the invention;

FIG. 11 illustrates a simplified flow diagram of a method of monitoringa processing system in real-time using one or more process models inaccordance with embodiments of the invention;

FIG. 12 illustrates a simplified flow diagram of a method of monitoringa monolayer deposition (MLD) system in real-time using one or moreprocess models in accordance with embodiments of the invention; and

FIG. 13 illustrates a simplified flow diagram of a method of creating aBIST table for the real-time monitoring of a processing system inaccordance with embodiments of the invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The invention relates to semiconductor manufacturing processes thatinvolve low-pressure processing. Examples of these processes includeatomic layer deposition (ALD/MLD,xLD) for films including Si₃N₄, Al₂O₃,Ta₂O₅, and HfSiON, chemical vapor deposition (CVD), and etch.

Such processes are conducted in both hot-wall and cold-wall processingchambers. These processing chambers are typically configured forsingle-wafer, multi-wafer, or batch operation. Such processing chamberscan be used for processing various types of wafers, including Siliconwafers and LCD panels.

A semiconductor processing system can include a thermal processingsystem, an etching system, a deposition system, a plating system, apolishing system, an implant system, a developing system, or a transfersystem, or a combination of two or more thereof. In addition, theprocess performed by the system can include a thermal process, anetching process, a deposition process, a plating process, a polishingprocess, an implant process, a developing process, or a transferprocess, or a combination of two or more thereof.

In accordance with the present invention, a processing system can bemonitored in real-time using a Built-In Self Test (BIST) table. In oneembodiment, one or more process parameters are changed or maintained,responses thereto are predicted and measured, and a dynamic estimationerror is calculated and compared to operational limits and/or warninglimits established for BIST rules in the BIST table. The process canthen be continued, paused or stopped depending on whether the dynamicestimation error is within the operational limits and/or within thewarning limits in the BIST table.

In one embodiment of the present invention, a method is provided for thedetection, diagnosis, and prediction of fault conditions to identifymalfunction and error conditions in the semiconductor equipment as wellas indicate drift and degradation that may lead to fault conditions.

In another or further embodiment, the present invention identifiesmalfunctions and/or error conditions in the processing system as well asindicates drift and degradation that may be leading to an impendingfault condition. Data to analyze the processing system can be obtainedeither in a“Passive Mode”, during a productive operation of the system,or in an“Active Mode”, where periodic self-tests are conducted duringidle time.

The invention will now be described with reference to the drawings. FIG.1 is an isometric view of a processing system in accordance withembodiments of the invention. The processing system 100 can comprise ahousing 101 that forms the outside walls of the processing system whenit is configured in a clean room. The interior of the housing 101 isdivided by a partition (bulkhead) 105 into a carrier-transferring area107 into and from which carriers 102 are conveyed and in which thecarriers 102 are kept, and a loading area 109 where wafers to beprocessed (not shown), such as semiconductor wafers W, located in thecarriers 102 are transferred to boats 103. The boats are loaded into orunloaded from a vertical type thermal processing chamber 104.

As shown in FIG. 1, an entrance 106 is provided in the front of thehousing 101 for introducing and discharging the carriers 102 by anoperator or an automatic conveying robot (not shown). The entrance 106is provided with a door (not shown) that can move vertically to open andclose the entrance 106. A stage 108 is provided near the entrance 106 inthe carrier-transferring area 107 for placing the carriers 102 thereon.

As shown in FIG. 1, a sensor mechanism 109 is provided at the rearportion of the stage 108 for opening a lid (not shown) of a carrier 102and detecting positions of and the number of the semiconductor wafers Win the carrier 102. In addition, there may be shelf-like storingsections 110 above the stage 108 for storing a plurality of the carriers102.

Two carrier-placing portions (transfer stages) 111 are provided invertically spaced positions as tables for placing the carriers 102thereon for transferring the semiconductor wafers W. Thus, thethroughput of the processing system 100 can be improved as one carrier102 can be exchanged at one carrier-placing portion 111 while thesemiconductor wafers W are transferred to another carrier 102 at theother carrier-placing portion 111.

A carrier transference mechanism 112 is arranged in thecarrier-transferring area 107 for transferring the carriers 102 to andfrom the stage 108, the storing sections 110, and the carrier placingportions 111. The carrier transference mechanism 112 comprises: anelevating arm 112 b which can be moved vertically by an elevatingmechanism 112 a provided on a side of the carrier-transferring area 107,and a transferring arm 112 c mounted on the elevating arm 112 b forsupporting the bottom of the carrier 102 to horizontally transfer thecarrier 102.

For example, the carrier 102 can be a closed type, which can house 13 or25 wafers and which can be hermetically closed by a lid (not shown). Thecarrier 102 can comprise a portable plastic container for housing andholding wafers W in multistory in horizontal attitude and in verticallyspaced relation by a prescribed pitch. In one embodiment, the diameterof the wafer W can be 300 mm. Alternatively, other wafer sizes may beused. The lid (not shown) is removably attached at the wafer-entranceformed in the front of the carrier 102 in such a manner that the lid cansealingly close the wafer-entrance.

Clean atmospheric air, which has passed through filters (not shown), canbe provided into the carrier-transferring area 107, so that thecarrier-transferring area 107 is filled with the clean atmospheric air.In addition, clean atmospheric air can also be provided into the loadingarea 109, so that the loading area 109 is filled with the cleanatmospheric air. Alternatively, an inert gas, such as nitrogen (N₂), issupplied into the loading area 109, so that the loading area is filledwith the inert gas.

As shown in FIG. 1, the partition 105 has two openings 113, upper andlower, for transferring a carrier 102. The openings 113 can be alignedwith the carrier-placing portions 111. Each opening 113 is provided witha lid (not shown) for opening and closing the opening 113. The opening113 is formed in such a manner that the size of the opening 113 issubstantially the same as that of the wafer-entrance of the carrier 102,so that semiconductor wafers W can be transferred into and from thecarrier 102 through the opening 113 and the wafer-entrance.

In addition, a notch aligning mechanism 115 is arranged below thecarrier-placing portions 111 and along a vertical central line of thecarrier-placing portion 111 for aligning notches (cut portions) providedat peripheries of the semiconductor wafers W i.e. for aligning thecrystalline directions of the semiconductor wafers W. The notch aligningmechanism 115 has an opening on the side of the loading area 107. Thenotch aligning mechanism 115 is adapted to align the notches of thesemiconductor wafers W transferred from the carrier 102 on thecarrier-placing portion 111 by a transferring mechanism 122.

The notch aligning mechanism 115 has two apparatus in vertically spacedpositions, and each apparatus can align the notches of the wafers W.Thus, the throughput of the processing system 100 can be improvedbecause one apparatus can transfer back the aligned wafers W to the boat103 while the other apparatus aligns other wafers W. Each apparatus maybe adapted to align plural, for example three or five wafers at a time,such that the time for transferring the wafers W can be substantiallyreduced.

The thermal processing chamber 104 is disposed in a rear and upperportion in the loading area 109. The thermal processing chamber 104 hasa chamber opening 104 a in the bottom thereof. A lid 117 is providedbelow the chamber 104. The lid 117 is adapted to be vertically moved byan elevating mechanism (not shown) for loading a boat 103 into andunloading it from the chamber 104 and for opening and closing thechamber opening 104 a. The boat 103, which can hold a large number of,for example 100 or 150 semiconductor wafers W in vertical equally spacedmultistory, is adapted to be placed on the lid 117. The boat 103 is madeof crystal or the like. The thermal processing chamber 104 is providedwith a shutter 118 at the chamber opening 104 a for closing the chamberopening 104 a while the lid 117 is taken off and the boat 103 isunloaded after the thermal processing. The shutter 118 is adapted tohorizontally pivot to open and close the chamber opening 104 a. Ashutter driving mechanism 118 a is provided to make the shutter 118pivot.

Still referring to FIG. 1, a boat-placing portion (boat stage) 119 isdisposed in a side region of the loading area 109 for placing the boat103 thereon when transferring semiconductor wafers W into and from theboat 103. The boat-placing portion 119 has a first placing portion 119 aand a second placing portion 119 b arranged between the first placingportion 119 a and the lid 117. A ventilating unit (not shown) isdisposed adjacent the boat-placing portion 119 for cleaning thecirculation gas (the clean atmospheric air or the inert gas) in theloading area 109 using filters.

A boat-conveying mechanism 121 is arranged between the carrier-placingportion 111 and the thermal processing chamber 104 in the lower portionin the loading area 109 for conveying the boat 103 between theboat-placing portion 119 and the lid 117. Specifically, theboat-conveying mechanism 121 is arranged for conveying the boat 103between the first placing portion 119 a or the second placing portion119 b and the lowered lid 117, and between the first placing portion 119a and the second placing portion 119 b.

A transferring mechanism 122 is arranged above the boat-conveyingmechanism 121 for transferring semiconductor wafers W between thecarrier 102 on the carrier-placing portion 111 and the boat 103 on theboat-placing portion 119, and more specifically, between the carrier 102on the carrier-placing portion 111 and the notch aligning mechanism 115,between the notch aligning mechanism 115 and the boat 103 on the firstplacing portion 119 a of the boat-placing portion 119, and between theboat 103 after the thermal processing on the first placing portion 119 aand a vacant carrier 102 on the carrier-placing portion 111.

As shown in FIG. 1, the boat-conveying mechanism 121 has an arm 123which can support one boat 103 vertically and move (expand and contract)horizontally. For example, the boat 103 can be conveyed in a radialdirection (a horizontal linear direction) with respect to the rotationalaxis of the arm 123 by synchronously rotating the arm 123 and a supportarm (not shown). Therefore, the area for conveying the boat 103 can beminimized, and the width and the depth of the processing system 100 canbe reduced.

The boat-conveying mechanism 121 conveys a boat 103 of unprocessedwafers W from the first placing portion 119 a to the second placingportion 119 b. Then, the boat-conveying mechanism 121 conveys a boat 103of processed wafers W from the lid 117 to the first placing portion 119a. Then, the boat-conveying mechanism 121 conveys the boat 103 ofunprocessed wafers W onto the lid 117. In this manner, the unprocessedwafers W are prevented from being contaminated by particles or gasescoming from the boat 103 of processed wafers W.

When a carrier 102 is placed on the stage 108 through the entrance 106,the sensor mechanism 109 detects the placing state of the carrier 102.Then, the lid of the carrier 102 is opened, and the sensor mechanism 109detects positions of and the number of the semiconductor wafers W in thecarrier 102. Then, the lid of the carrier 102 is closed again, and thecarrier 102 is conveyed into a storing section 110 by means of thecarrier transference mechanism 112.

A carrier 102 stored in the storing section 110 is conveyed onto thecarrier-placing portion 111 at a suitable time by means of the carriertransference mechanism 112. After the lid of the carrier 102 on thecarrier-placing portion 111 and the door of the opening 113 of thepartition 105 are opened, the transferring mechanism 122 takes outsemiconductor wafers W from the carrier 102. Then, the transferringmechanism 122 transfers them successively into a vacant boat 103 placedon the first placing portion 119 a of the boat-placing portion 119 viathe notch aligning mechanism 115. While the wafers W are transferred,the boat-conveying mechanism 121 is lowered to evacuate from thetransferring mechanism 122, so that the interference of theboat-conveying mechanism 121 and the transferring mechanism 122 isprevented. In this manner, the time for transferring the semiconductorwafers W can be reduced, so that the throughput of the processing system100 can be substantially improved.

After the transference of the wafers W is completed, the transferringmechanism 122 can move laterally from an operating position to a holdingposition in the other side region of the housing 101.

After the thermal processing is completed, the lid 117 is lowered, andthe boat 103 and the thermally processed wafers are moved out of thethermal processing chamber 104 into the loading area 109. The shutter118 hermetically closes the opening 104 a of the chamber immediatelyafter the lid 117 has removed the boat 103. This minimizes the heattransfer out of the thermal processing chamber 104 into the loading area109, and minimizes the heat transferred to the instruments in theloading area 109.

After the boat 103 containing the processed wafers W is conveyed outfrom the thermal processing chamber 104, the boat-conveying mechanism121 conveys another boat 103 of unprocessed wafers W from the firstplacing portion 119 a to the second placing portion 119 b. Then, theboat-conveying mechanism 121 conveys the boat 103 containing theprocessed wafers W from the lid 117 to the first placing portion 119 a.Then, the boat-conveying mechanism 121 conveys the boat 103 ofunprocessed wafers from the second placing portion 119 b onto the lid117. Therefore, the unprocessed semiconductor wafers W in the boat 103are prevented from being contaminated by particles or gases coming fromthe boat 103 of processed wafers W when the boats 103 are moved.

After the boat 103 of unprocessed wafers W is conveyed onto the lid 117,the boat 103 and the lid 117 are introduced into the thermal processingchamber 104 through the opening 104 a after the shutter 118 is opened.The boat 103 of unprocessed wafers W can then be thermally processed. Inaddition, after the boat 103 of processed wafers W is conveyed onto thefirst placing portion 119 a, the processed semiconductor wafers W in theboat 103 are transferred back from the boat 103 into the vacant carrier102 on the carrier-placing portion 111 by means of the transferringmechanism 122. Then, the above cycle is repeated.

Setup, configuration, and/or operational information can be stored bythe processing system 100, or obtained from an operator or anothersystem, such as a factory system. BIST tables can be rule-based and canbe used to specify the action taken for normal processing and theactions taken on exceptional conditions. Configuration screens can beused for defining and maintaining BIST tables. The operational limits,operational conditions, the BIST rules associated with them can bestored and updated as required. Documentation and help screens can beprovided on how to create, define, assign, and maintain the BIST tables.

BIST tables can be used to determine when a process is paused and/orstopped, and what is done when a process is paused and/or stopped. Inaddition, BIST tables can be used to determine when to change a processand how to change the process. Furthermore, the BIST tables can be usedto determine when to select a different dynamic/static model and how tocreate a new operational limit, and/or a new BIST rule in the process.In general, BIST tables allow system operation to change based on thedynamic state of the system.

In one embodiment, processing system 100 can comprise a systemcontroller 190 that can include a processor 192 and a memory 194. Memory194 can be coupled to processor 192, and can be used for storinginformation and instructions to be executed by processor 192.Alternatively, different controller configurations can be used. Inaddition, system controller 190 can comprise a port 195 that can be usedto couple processing system 100 to another system (not shown).Furthermore, controller 190 can comprise input and/or output devices(not shown) for coupling the controller 190 to other elements of thesystem.

In addition, the other elements of the system can comprise processorsand/or memory (not shown) for executing and/or storing information andinstructions to be executed during processing. For example, the memorymay be used for storing temporary variables or other intermediateinformation during the execution of instructions by the variousprocessors in the system. One or more of the system elements cancomprise means for reading data and/or instructions from a computerreadable medium. In addition, one or more of the system elements cancomprise means for writing data and/or instructions to a computerreadable medium.

Memory devices can include at least one computer readable medium ormemory for holding computer-executable instructions programmed accordingto the teachings of the invention and for containing data structures,tables, records, rules, or other data described herein. Systemcontroller 190 can use data from computer readable medium memory togenerate and/or execute computer executable instructions. The processingsystem 100 can perform a portion or all of the methods of the inventionin response to the system controller 190 executing one or more sequencesof one or more computer-executable instructions contained in a memory.Such instructions may be received by the controller from anothercomputer, a computer readable medium, or a network connection.

Stored on any one or on a combination of computer readable media, thepresent invention includes software for controlling the processingsystem 100, for driving a device or devices for implementing theinvention, and for enabling the processing system 100 to interact with ahuman user and/or another system, such as a factory system. Suchsoftware may include, but is not limited to, device drivers, operatingsystems, development tools, and applications software. Such computerreadable media further includes the computer program product of thepresent invention for performing all or a portion (if processing isdistributed) of the processing performed in implementing the invention.

In addition, at least one of the elements of the processing system 100can comprise a graphic user interface (GUI) component (not shown) and/ora database component (not shown). In alternate embodiments, the GUIcomponent and/or the database component are not required. The userinterfaces for the system can be web-enabled, and can provide systemstatus and alarm status displays. For example, a GUI component (notshown) can provide easy-to-use interfaces that enable users to: viewstatus; create and edit SPC charts; view alarm data; configure datacollection applications; configure data analysis applications; examinehistorical data; review current data; generate e-mail warnings; runmultivariate models; view diagnostics screens; and view/create/edit BISTtables in order to more efficiently troubleshoot, diagnose, and reportproblems with the processing system 100.

FIG. 2 is a partial cut-away schematic view of a portion of asemiconductor wafer processing system 200 in accordance with embodimentsof the invention. In the illustrated embodiment, a processing system205, an exhaust system, 210, a gas supply system 260, and a controller290 are shown.

The processing system 205 can comprise a vertically oriented processingchamber (reaction tube) 202 having a double structure including an innertube 202 a and an outer tube 202 b which are formed of, e.g., quartz,and a cylindrical manifold 221 of metal disposed on the bottom ofprocessing chamber 202. The inner tube 202 a is supported by themanifold 221 and has an open top. The outer tube 202 b has its lower endsealed air-tight to the upper end of the manifold 221 and has a closedtop.

In the processing chamber 202, a number of wafers W (e.g., 150) aremounted on a wafer boat 223 (wafer holder), horizontally one aboveanother at a certain pitch in a shelves-like manner. The wafer boat 223is held on a lid 224 through a heat insulation cylinder (heat insulator)225, and the lid 224 is coupled to moving means 226.

The processing system 205 can also comprise a heater 203 in the form of,e.g., a resistor disposed around the processing chamber 202. The heater203 can comprise five stages of heaters 231-235. Alternatively, adifferent heater configuration can be used. The respective heater stages231-235 are supplied with electric power independently of one anotherfrom their associated electric power controllers 236-240. The heaterstages 231-235 can be used to divide the interior of the processingchamber 202 into five zones.

A gas supply system 260 is shown coupled to the controller 290 and theprocessing system 205. The manifold 221 has a plurality of gas feedpipes 241-243 for feeding gases into the inner tube 202 a. In oneembodiment, dichlorosilane, ammonium, and nitrogen can be fed to therespective gas feed pipes 241, 242, 243 through flow rate adjusters 244,245, 246, such as mass flow controllers (MFCs). Alternatively, amulti-zone gas injection system can be used and/or other process gassesmay be used.

An exhaust pipe 227 is connected to the manifold 221 for the exhaustionthrough the gap between the inner pipe 202 a and the outer pipe 202 b.The exhaust pipe 227 is connected to an exhaust system 210 that caninclude a vacuum pump (not shown). A pressure adjuster 228 including acombination valve, a butterfly valve, valve drivers, etc. can beinserted in the exhaust pipe 227 for adjusting a pressure in theprocessing chamber 202. Alternatively, a different configuration may beused for the exhaust system 210.

The processing system 205 can also comprise a number of sensors. In theillustrated embodiment, five inner temperature sensors (thermocouples)251-255 are disposed on the inside of the inner tube 202 a in verticalalignment with each other. The inner temperature sensors 251-255 arecovered with, e.g., quartz pipes for the prevention of metalcontamination of semiconductor wafers W. The inner temperature sensors251-255 are arranged corresponding to the five zones. Alternatively, adifferent number of zones may be used, a different number of innertemperature sensors may be used, and the inner sensors may be positioneddifferently. In another embodiment, optical techniques can be used tomeasure temperature.

A plurality of outer temperature sensors (thermocouples/temperaturemeters) 261-265 is disposed on the outside of the outer tube 202 b invertical alignment with each other. The outer temperature sensors261-265 can also be arranged corresponding to the five zones.Alternatively, a different number of zones may be used, a differentnumber of outer temperature sensors may be used, and the outer sensorsmay be positioned differently.

The controller 290 can be used to control treatment parameters, such asa temperature of a treatment atmosphere, a gas flow rate, and pressurein the processing chamber 202. The controller 290 receives outputsignals of the inner temperature sensors 251-255 and outer temperaturesensors 261-265 to output control signals to the electric powercontrollers 236-240, the pressure adjuster 228 and the flow rateadjusters 244-246.

Setup, configuration, and/or operational information can be stored bythe controller 290, or obtained from an operator or another controller,such as a controller 190 (FIG. 1). Controller 290 can also use BISTtables to determine the action taken for normal processing and theactions taken on exceptional conditions. Controller 290 can manageconfiguration screens that can be used for defining and maintaining BISTtables. Controller 290 can store and update the BIST tables as required.Controller 290 can manage documentation and help screens that can beused to create, define, assign, and maintain the BIST tables.

Controller 290 can use BIST tables in real time to determine when aprocess is paused and/or stopped, and what is done when a process ispaused and/or stopped. In addition, BIST tables can be used to determinewhen to change a process and how to change the process.

In one embodiment, controller 290 can include a processor 292 and amemory 294. Memory 294 can be coupled to processor 292, and can be usedfor storing information and instructions to be executed by processor292. Alternatively, different controller configurations can be used. Inaddition, system controller 290 can comprise a port 295 that can be usedto couple controller 290 to another computer and/or network (not shown).Furthermore, controller 290 can comprise input and/or output devices(not shown) for coupling the controller 290 to the processing system205, exhaust system, 210, and gas supply system 260.

Controller 290 can comprise means for reading data and/or instructionsfrom a computer readable medium. In addition, controller 290 cancomprise means for writing data and/or instructions to a computerreadable medium.

Memory 294 can include at least one computer readable medium or memoryfor holding computer-executable instructions programmed according to theteachings of the invention and for containing data structures, tables,records, rules, or other data described herein. Controller 290 can usedata from computer readable medium memory to generate and/or executecomputer executable instructions. The processing system 205, exhaustsystem, 210, a gas supply system 260, and a controller 290 can perform aportion or all of the methods of the invention in response the executionof one or more sequences of one or more computer-executable instructionscontained in a memory. Such instructions may be received by thecontroller from another computer, a computer readable medium, or anetwork connection.

Stored on any one or on a combination of computer readable media, thepresent invention includes software for controlling the processingsystem 205, exhaust system, 210, gas supply system 260, and a controller290, for driving a device or devices for implementing the invention, andfor enabling one or more of the system components to interact with ahuman user and/or another system. Such software may include, but is notlimited to, device drivers, operating systems, development tools, andapplications software. Such computer readable media further includes thecomputer program product of the present invention for performing all ora portion (if processing is distributed) of the processing performed inimplementing the invention.

Controller 290 can comprise a GUI component (not shown) and/or adatabase component (not shown). In alternate embodiments, the GUIcomponent and/or the database component are not required. The userinterfaces for the system can be web-enabled, and can provide systemstatus and alarm status displays. For example, a GUI component (notshown) can provide easy to use interfaces that enable users to: viewstatus; create and edit charts; view alarm data; configure datacollection applications; configure data analysis applications; examinehistorical data, and review current data; generate e-mail warnings;view/create/edit/execute dynamic and/or static models; view diagnosticsscreens; and view/create/edit BIST tables in order to more efficientlytroubleshoot, diagnose, and report problems.

During a process, the controller 290 can cause one or more processparameters to change form one value to another value. A real-timedynamic model can be established for this particular systemconfiguration based on the type of vertical wafer boat 223, the type,position, and quantity of wafers W, the type of thermal processingchamber 202, and the recipe to be performed.

The real-time dynamic pressure model can be executed to generate apredicted dynamic pressure response for the processing chamber duringthe process. In addition, a measured dynamic pressure response can becreated for the processing chamber during the process, and a dynamicestimation error can be determined using a difference between thepredicted dynamic response and the measured dynamic response.Furthermore, the dynamic estimation error can be compared to operationallimits established for one or more BIST rules in a BIST table. Theprocess can be stopped when the dynamic estimation error is not withinoperational limits established for at least one of the BIST rules in aBIST table, and the process can continue when the dynamic estimationerror is within operational limits established for at least one of theBIST rules in a BIST table.

During operation, the temperatures of wafers W in the respective zonesare estimated, and adaptive methods are used to control the heaterstages 231-235 so that the corrected wafer temperatures can be equal totemperatures indicated by the recipe. When the temperature increase iscompleted, the adaptive control is used to retain the temperatures ofthe respective zones. Techniques for controlling a heating apparatususing models are disclosed in U.S. Pat. No.6,803,548, entitled“Batch-type Heat Treatment Apparatus and Control Method for theBatch-type Heat Treatment Apparatus, which is incorporated by referenceherein.

Controller 290 can also create a measured static and/or dynamic responseusing data from the inner temperature sensors 251-255, the outertemperature sensors 261-265, the electric power controllers 236-240, thepressure adjuster 228, or the flow rate adjusters 244-246, or acombination thereof.

FIG. 3 illustrates a simplified block diagram of a processing system inaccordance with embodiments of the invention. In the illustratedembodiment, a processing system 300 is shown that comprises a system310, a controller 320, a dynamic model 330, and a comparator 340. Inaddition, actuation variables (AV) are shown, and these are thevariables that have a fixed setpoint (SP) in the recipe or are generatedin real-time by the controller 320 based on a setpoint in the recipe.For example, heater power, mass flow rate, and exhaust valve angle.

Two types of process variables (PV) are illustrated, and these areprocess conditions in the equipment as a result of the actuationvariables (AV). Examples of process variables (PV) include chamber orwafer temperatures, chamber chemistry, reactant concentration at thewafers, and film thickness on the wafer. The process variables (PV) canbe classified as measured process variables (MPV) that are measuredusing sensors and general process variables (GPV) that are not measuredby sensors. Of the ones that are measured, some can be directlycontrolled via the controller 320—these are controlled process variables(CPV).

The AV, MPV, and SP are available in real-time. By definition, the GPVare not available (not measured); their effect may be deduced only byend-of-run measurements. For example, in a batch processing chamber,real-time data is available for chamber pressure, mass flow rates andtheir setpoints, valve angles, and chamber temperature for each zone.

During system operation, error conditions can occur. For example, thetypes of error conditions can include a component failure, where anactive, passive, or software component fails to perform a required task;a component degradation, where the performance of an active, passive, orsoftware component is degraded, and a failure can occur in the nearfuture if the degraded performance is not corrected; and aconfigurations error, where an active, passive, or software component isnot configured properly.

The processing system and/or the system components can be in one of twostates when operational, a processing state in which the system and/orthe system components are processing wafers and/or wafers; and an idlestate in which the system and/or one or more of the system componentsare waiting to process wafers and/or substrates. In an alternateembodiment, a maintenance state may also be used in which the systemand/or one or more of the system components is off-line for amaintenance, calibration, and/or repair time.

These two states provide unique opportunities to perform operations forcreating and/or modifying a BIST table. In the passive mode, during theprocessing state, one or more of the processes can “observe” thereal-time system response, but cannot make changes to the processingconditions. For example, the system response can be observed, andprocessing conditions and error conditions can be determined. Inaddition, dynamic and/or static models can be executed, and the BISTrules, the operational conditions, operational limits, and tolerancevalues in a BIST table can be verified. In addition, new BIST rules, newoperational conditions, new operational limits, and/or new tolerancevalues can be created and stored in a BIST table.

In the idle mode, one or more of the processes can make changes to theprocessing conditions since no product wafers are being processed.During the idle mode, one or more of the processes can create processingconditions as necessary to detect and diagnose degradations and faultconditions. These degradations and fault conditions can be used tocreate and/or modify the BIST rues, the operational conditions, theoperational limits, and/or the tolerance values in a BIST table. Inparticular, one or more of the processes may select process parametersto magnify an error condition, rather than to hide or compensate for it.In the idle mode, the system can be operated using productionconditions, or the system can be operated using non-productionconditions (e.g., no wafers in the chamber, no reactant gases flowing,etc.) In addition, one level of tests can be conducted at the componentlevel, and these tests can also be static or dynamic. For example,heater resistance can be monitored for signs of any degradation.

Static measurements are one way to detect errors. However, drift anddegradation may be small for multiple parameters, but they have anoverall impact on system performance.

The system dynamic performance is a composite picture of the systemparameters that can be dependent on a number of variables. For example,a system response can be a function of an active, passive, or softwarecomponent. Deviation in one or more of these components can lead toerrors. For better detection and diagnosis, a “system level” approachcan be used.

Recipes can be used in a system level, and a typical recipe provides thesetpoints (SP) for the measured process variables (MPV), including thecontrolled process variables (CPV), and the system controller cancontrol the actuation variables (AV) to reduce the error between the CPVand SP, where the Error=SP−CPV.

In addition, rules can be used to specify an acceptable range of the CPVduring certain critical steps. An alarm is generated if the CPV goes outof this range. For example:CPV−Lower Bound (LB)>Alarm Operational limit (1)Upper Bound (UB)−CPV>Alarm Operational limit (2)

However, this approach only determines the controllers “ability” to keepthe error small—it does not determine if the equipment is functioningproperly. In particular, it does not address what is happening with thegeneral process variables, and hence, the end-of-run parameters.

In one embodiment, the BIST tables can be used to determine if thesystem and/or the system components are behaving “as-designed” from thereal-time data and dynamic models of the system components. Dynamicmodels provide the response of the system “as designed,” and can be usedfor detecting error conditions. For example, an error can be computedusing the difference between the modeled response (IPV) and the measuredresponse as shown below:Error=IPV−MPV

A warning and/or fault can be created if this error is greater thanpre-set operational limits. The BIST table can include BIST rules,operational conditions, operational limits, and tolerance values.

In an “active mode”, procedures based on the data in BIST tables can beused to create conditions to magnify the error between the modeledresponse and measured response in the appropriate regime of the PV. Insuch dynamic conditions, variation between the modeled and measured isamplified. Under static or steady conditions, the errors can appear as“bias” errors and can be swamped by measurement noise. Active mode cansignificantly increase the probability of true alarms.

For example, for a processing system, the models used for BIST tablescan be related to various real-time data sets collected from the system;these include setpoints, MFC flow rates, pressure measurements from the0-10 Torr and 0-1000 Torr gauges, valve angle, temperature data, andpressure control parameters.

The models include both dynamic (transient) and steady-state behavior.For example, dynamic behavior models pressure rise rate. To describe themathematical model further, notation shown in Table 1 can be used: TABLE1 Parameter Description p_(i) i^(th) MFC gas flow rate (sccm) v Valveangle opening (%) P_(c) Chamber pressure (mTorr)

The rate of change for chamber pressure {dot over (P)}_(c) as a functionƒ of gas flows and valve angle can be modeled as follows:{dot over (P)} _(c)=ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

A special condition exists when the valve is fully closed—in this case,the pressure rise rate becomes independent of the pressure controller.For this condition, the chamber pressure rise rate {dot over (P)}_(c)can be:{dot over (P)} _(c) 32 ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v=0)

Given this model, one method for individually estimating MFC flow ratesis to use an inverse function:p _(i)=ƒ₁ ⁻¹({dot over (P)} _(c))

In addition, the steady-state behavior can be modeled as follows:P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

This model can be used to estimate a parameter given the rest of theparameters, that is:p _(i) =g ₁ ⁻¹(P _(c) ,v),v=g ₁ ⁻¹(p ₁ ,p ₂ , . . . , p _(n) ,P _(c)), andP _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

Thus, these models provide multiple estimates of the process parametersfor a number of different operational conditions. The inference logiccan be used to examine the estimated parameters to generate diagnosticsbased on the BIST rules, the operational conditions, and/or operationallimits in a BIST table.

In one embodiment, a method can be established to capture the dynamicand steady-state behavior of the gas-flow system coupled to theprocessing system. The method involves running a “model-development”recipe on the processing system and/or system components. The recipe isdesigned to operate under a variety of conditions, as follows:

1) system dynamic response under automatic pressure control (APC);

2) system dynamic and steady-state response under manual valve control(MVC);

3) base pressure with valve fully open; and

4) leak rate with valve fully closed.

In the set of tests to determine the system response under APC, thepressure setpoint can be changed, and the change in chamber pressure forvarious gas flow rates can be analyzed. For example, the followingchanges can be made:

1) Step change in pressure setpoint from zero to 3 Torr,

2) Step change from 3 to 6 Torr, and

3) Step change from 6 to 9 Torr.

When the pressure setpoint is changed, from 0 to 3 Torr, the pressurecontroller manipulates the main valve opening to achieve the targetpressure. Initially, the controller action completely shuts the valve.Under these conditions, the pressure rise rate also becomes a functionof gas flow rate, and is independent of the valve angle. Exemplaryresults are shown in FIG. 4, FIG. 5, and FIG. 6. FIG. 4 shows thechamber pressure transient behavior for a pressure setpoint change from0 to 3 Torr. FIG. 5 shows the chamber pressure transient behavior for apressure setpoint change from 3 to 6 Torr. FIG. 6 shows the chamberpressure transient behavior for a pressure setpoint change from 6 to 9Torr.

There are three sets of data—for each pressure step response, thepressure rise rate is measured for a 200, 250, and 300 sccm gas flowrate. This data can be used to obtain a consistent mathematical model ofpressure rise rate vs. gas flow rate. For example, a linear relationshipcan be used:y=ax+b,

where y=pressure rise rate (mTorr/sec) and x=gas flow rate (sccm). Alinear least square fit yielded the results in Table 2. TABLE 2Parameter Parameter Test case “a” “b” 0 to 3 Torr 0.292 −1.4 3 to 6 Torr0.288 −0.25 6 to 9 Torr 0.289 −0.47

These results are also shown in FIG. 7 in which the rise rate is shownas a function of gas flow rate for the three step response test cases.

The parameter “b” should be ideally equal to zero—when there is no gasflow, the pressure rise rate should be zero. The measured value is avery small number around 1 sccm. The main parameter is “a”. It is clearfrom the data in Table 2 that in this operating regime, the pressurerise rate can be modeled with a single set of parameters “a” and “b”,independent of the gas flow rate, and this is one of the sub-models usedin the software for a BIST table. For example, the measured pressurerise rate is approximately equal to 75 mTorr/sec when the estimated gasflow rate is approximately equal to 258.6 sccm.

The system response under MVC can be determined, and a relationship ofsteady state pressure P_(c) as a function of gas flows and valve anglecan be obtained using:P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

This function is expected to be quite nonlinear (unlike the linearfunction obtained for the pressure rise rate). In one case, specificvalues of this function can be empirically obtained under the followingcombination of conditions: for MFC flow rates of 200, 250, and 300 sccmand valve angles of 3.3, 4.3, and 5.3%. For example, the values obtainedon one system are shown in Table 3, and the chamber pressure as afunction of flow rates at various valve angles is illustrated in FIG. 8.TABLE 3 3.3% 4.3% 5.3% 200 423 270 206 250 506 321 244 300 578 367 279

In one embodiment, a real-time estimator methodology can be used.Alternatively, other methods may be used. The semiconductor processingsystem and/or one or more of the system components or subsystemcomponents can be modeled using a set of nonlinear differentialequations {dot over (x)} and an output equation y as follows:{dot over (x)}=ƒ( x,p,u)+wy=g(x,p,u)+vwhere: x is the state vector which can consist of temperatures,pressures, and reactant states; the vector p consists of modelparameters, such as heat capacity, thermal conductivity, and rateconstants; the vector u consists of input applied to the process, suchas heater powers; w is the additive white noise with zero mean, E(w)=0(E(•) denotes the expectation operator), v is the additive white noisewith zero mean, and E(v)=0.

Given the initial state x₀, input u, and parameters p, the differentialequations can be integrated to compute the evolution of the state.

In addition, the models can be linearized for real-time applications.The linearization may lead to one or a set of models that describe thedynamics of the system along a nominal trajectory. These linear modelsare represented in state-space form by matrices A_(i), B_(i), and C_(i)for each ith time interval. Thus, the nonlinear models are replaced by asequence of discrete-time linear models:x _(k+1) =A _(i) x _(k) +B _(i) u _(k) +w _(k)y _(k) =C _(i) x _(k) +v _(k)where k is a time index. The covariance of the initial state P₀ isE{x₀x₀ ^(T)}=P₀, where T is the transposition operator.

A convenient method to build a real-time estimator is using Kalmanfilters matrices, L_(i), which gives:{circumflex over (x)} _(k+1) =A _(i) {circumflex over (x)} _(k) +B _(i)u _(k) +L _(i)(y−C _(i) {circumflex over (x)})ŷ _(k) =C {circumflex over (x)} _(k) +v _(k)where ˆ indicates an estimated value.

When performing a steady-state check, the dynamic model of the system(without the noise terms) can be used, and the set of nonlineardifferential equations {dot over (x)} and an output equation y can be asfollows:{dot over (x)}=ƒ( x,p,u)y=g(x,p,u)

At some steady state, {dot over (x)}=0, and the steady-state values forthe state, input, and output will be x_(s), u_(s), and y_(s),respectively. Using known steady state values of the input and outputfor a reference system (e.g., u_(ref) and y_(ref)), the steady-statevalues for any given system can be monitored and compared to thereference. In particular, if the feedback controller drives the systemoutput to y_(ref), the value of u_(s) can be checked; that is:

-   -   Drive the outputs to reference value y_(s)→y_(ref), and hence        ∥y_(s)−y_(ref)∥≦ε    -   Check the inputs to the reference value Is ∥u_(s)−u_(ref)∥≦ε?        ε is selected to be a sufficiently small value for the        particular system.

If the difference is small, then the system under test (SUT) isoperating like the reference system; otherwise, a possibility of anerror condition is indicated.

As a first example, consider a thermal processing chamber with fivezones; suppose on the thermal processing chamber it has been determinedthat when all the zones are at 600° C., the heater power should be asshown in Table 4. TABLE 4 Zone Power (W) 1 1200 2 1300 3 1400 4 1400 51300

When a thermal processing chamber at the same five 600° C. temperaturezones is reporting a heater power of 2600W in zone 5, it is clear thatsome sort of error condition is indicated—the error condition could bewith the heater zone, o-rings, etc., and must be diagnosed with furthertests.

In one embodiment, a dynamic response check can be performed. Asdescribed herein, one way to detect error is to monitor the dynamicresponse of the system and compare it to the reference. For example, adynamic real-time estimator can be used for this purpose. Consider alinear estimator created with the reference system, where the estimatesof the output are given by:ŷ _(k) C{circumflex over (x)} _(k) +v _(k)

When the SUT is producing outputs y_(k), a check can be performed todetermine if the two are close enough:

-   -   Check the SUT output with estimates of reference system        ${Is}\quad{\sum\limits_{i - 1}^{n}{\quad{y_{k} - {\hat{y}}_{k}}}}$    -    reasonably small?

Thus, these models provide multiple estimates of the process parameters.The inference logic can be used to examine the estimated parameters togenerate diagnostics based on the BIST rules, the operationalconditions, and operational limits in the BIST table.

As a second example, when examining low-pressure processes, a monolayerdeposition (MLD) process recipe can be used. An exemplary MLD processrecipe is shown in Table 5. Note that the process parameters of therecipe are selected for illustrative purposes only.

The steps of the recipe shown below focus on the portion of the recipeused to create a monolayer of the desired film on the wafer(s). Thisportion is repeated several times to achieve desired film thickness. Forexample, a recipe may call for 100 repetitions of such a sub-cycle.Reduction in process time for each such cycle can lead to substantialsaving in overall cycle time. TABLE 5 Temp Step Time (deg Pressure BackG_(I) R_(A) (G_(I)) R_(B) (G_(I)) # Name (sec) C.) (Torr) (sccm) (sccm)(sccm) 1 R_(A) Step 150 500 1 100 250  (100) 2 Purge 11 90 500 MV Open100 (100) (2000) 3 Purge 12 30 500 1 100 (100) (1000) 4 R_(B) Step 150500 1 100 (100)  100 5 Purge 21 90 500 MV Open 100 (100) (2000) 6 Purge22 30 500 1 100 (100) (1000)

In one set of operational conditions, the chamber can be evacuated to alow pressure of one Torr, and this can be followed by a repetition ofgas flow steps including precursor gases and purging gasses. During theR_(A) step shown in Table 2, the setpoint of the R_(A) MFC is set to 250sccm and held at this value for 150 sec. During this time, the pressurecontroller is active with a setpoint of one Torr. In the next step, theR_(A) MFC is closed, the G_(I) MFC is set to 2000 sccm, and the mainexhaust valve is opened. Likewise, for the R_(B) step, the setpoint ofthe R_(B) MFC is set to 100 sccm and held at that value for 150 sec. Thesecond purge step is similar to the first purge step.

In one embodiment, the present invention provides a controller operatingin real-time that includes hardware, software, and BIST applications formonitoring the following process parameters and their associated systemcomponents: pressure setpoints (mTorr), actual chamber pressures(mTorr), valve angle setpoints, actual valve angles (%), reactant MFCsetpoints (sccm), other MFC setpoints (sccm), inert gas flow MFCsetpoints (sccm), temperature setpoints (° C.), actual temperatures (°C.), processing times (secs), actual times (secs), valve positions,reactant concentrations, chamber chemistry, and wafer position.

In a simplified procedure, the methodology can be described as thefollowing: first, the chamber is purged of the reactants by flowing N₂through the reactant MFCs. The main exhaust valve is opened for a periodof time and then, the main exhaust valve is closed and the reactant flowis turned on. The reactant MFC setpoint is set to the desired flowvalue. Based on the set flow rate—the chamber pressure is expected torise at a given rate—based on the MFC setpoint. The valve can remainclosed for a certain duration, and then, the valve can respond to thesetpoint on the chamber pressure under automatic pressure control.

In a simplified example, a simplified model of a thermal processingchamber can be created that relates a first process parameter, such asGas Flow Rate (GFR), to the rate of change of a second processparameter, such as a Pressure Rise Rate (PRR). Then, for any givenprocess recipe step while and/or after a reactant gas flow isintroduced, a Measured Pressure Rise Rate (MPRR) can be obtained bymonitoring the real-time process parameters. Next, using the MPRR andthe model described above, a Measured Gas Flow Rate (MGFR) can becalculated. Then, the MGFR can be compared to the Expected Gas Flow Rate(EGFR)—this expected gas flow rate can be the setpoint in the recipe. Ifthere is a mismatch between the MGFR and EGFR, then a degraded processcondition can be expected. The severity of mismatch can be used toestablish warning or fault conditions.

In one embodiment, the present invention provides a method formonitoring the dynamic and steady-state behavior of the processingsystem and associated gas-flow system. The method involves running a“model-development” recipe on the processing system—the recipe isdesigned to operate under a variety of condition in order to produce anumber of new BIST rules, new operational conditions, new operationallimits, and/or new tolerance values in a BIST table. Alternatively,other processing systems may be monitored.

Requirements for the processing of wafers can include tight criticaldimension (CD) control, tight profile control, and tight uniformitycontrol—both wafer-in-wafer and wafer-to-wafer. In addition, filmthickness and file uniformity can be critical. For example, variationsin CD measurements, profile measurements, and film uniformitymeasurements may be caused by variations in thermal profile across waferzones and variations in thermal response from wafer to wafer.

Typically, bare silicon wafers are relatively flat and are manufacturedwithin tight specifications. However, multiple films are deposited onwafers during multiple thermal processes, and as a result, wafers canacquire significant curvature. Wafer curvature can have an adverseimpact on film uniformity and/or CD uniformity by creating problemsduring processing, including a deposition process.

A BIST table can be used to detect wafer position errors and reject awafer when it has excess curvature. Real-time data from one or moremeasurement devices can be used in a “mathematical model” to estimateand/or compensate for wafer curvature, and the model can be static ordynamic, linear or nonlinear.

In one embodiment, the monitoring system uses the dynamic response ofthe chamber as flat and/or warped wafers are positioned within and/orprocessed in the thermal processing chamber to detect, diagnose, and/orpredict system performance. For example, wafers with differentcurvatures create different dynamic thermal responses when they arepositioned within and/or processed in the thermal processing chamber.

In addition, other embodiments can be designed for both real-time andnon-real-time comparisons. In a real-time method, system performance canbe estimated and monitored in real time during processing of the wafer.In a non-real-time method, the data can be processed at a later time,and the system performance can be estimated and monitored after one ormore of the wafers have been processed. In other embodiments, virtualsensors can be used to “measure” wafer temperatures in real-time andeliminate the need for instrumented wafers during production. Forexample, a virtual sensor can comprise a dynamic model component or areal-time model, a physical sensor component that measures a physicalvariable such as temperature, a manipulated variables component thatregulates a variable such as applied voltage or power to the heater, anda software algorithm component that relates the dynamic model componentin conjunction with information from the physical sensors and themanipulated variables. The virtual sensor may be viewed as a compounddevice comprising an algorithm-based consolidation of information frommultiple “physical” sensors. The virtual sensor is an adaptive devicethat can provide historical data, real-time data, and predictive data.

FIG. 9 illustrates a schematic representation of an embodiment of thedynamic model 904 characterizing one or more of the responses of aprocessing system in accordance with an embodiment of the invention. Inthe illustrated embodiment, four nodes or model components (M₁, M₂, M₃,and M₄) 948, 950, 952, 954 are shown. However, in alternativeembodiments of the invention, a different number of model components maybe used, and the model components may be arranged with a differentarchitecture.

In addition, the dynamic model 904 receives control inputs (U) 962, suchas heater power, chamber pressure, gas flow, and wafer information. Themodel also receives disturbance inputs (D) 956, such as unmeasuredvariations. The model determines regulated outputs (Z) 958, such aswafer temperatures, and measured outputs (Y) 960, such as chambertemperatures. The model structure may be expressed as Z=M₁U+M₃D andY=M₂U+M₄D. Alternatively, a different expression for the model structuremay be used.

The dynamic model 904 tracks the “state” of the system, and relates theinputs 962 to outputs 958, 960 in real-time. For example, U and Y may bemeasured, and by using the dynamic model 904, D may be estimated usingY=M₂U+M₄D_(est) and Z may be estimated using Z_(est)=M₁U+M₃D_(est).

When creating the dynamic model 904, wafer position, wafer curvature,and chamber effects may be incorporated into the model. For example,dynamic models 904 can be created using first principles models based onheat transfer, gas flow, and reaction kinetics, or on-line modelscreated with real-time data collected from a processing system, such asa thermal processing system and/or MLD system.

During model development, a first principles model may be implementednumerically on a suitable microprocessor in a suitable softwaresimulation application, such as Matlab. The software application resideson a suitable electronic computer or microprocessor, which is operatedso as to perform the physical performance approximation. However, othernumerical methods are contemplated by the present invention.

A model-based linear or nonlinear multivariable control approach may beused to model the thermal doses in which the controller comprises amathematical model of the system to be controlled. The multivariablecontroller may be based on any of the modern control design methods suchas linear-quadratic-gaussian (LQG) method, linear quadratic regulator(LQR) method, H-infinity (H-inf) method, etc. The thermal dose model maybe either linear or nonlinear and either SISO or MIMO. The multivariablecontrol approach (i.e., MIMO) considers all inputs and their effects onthe outputs. Several other approaches for modeling the thermal doses areavailable, such as physical models, and data-driven models.

FIG. 10 illustrates a simplified schematic drawing for a semiconductorprocessing system in accordance with embodiments of the invention. Inone embodiment, the processing equipment used in low-pressure processingcan include a processing chamber and gas flow system to create desiredgas flow conditions in the processing chamber. In the illustratedembodiment, a simplified schematic view of a TELFORMULA® System fromTokyo Electron Limited is shown that includes a number of componentsthat enable both atmospheric and low-pressure operation, with a varietyof gas species.

In the illustrated embodiment, a gas supply system is shown thatincludes mass flow controllers (MFC) 15, mass flow meters (MFM) 20,inputs 25, outputs 35, supply lines 55, and interlock valves 10.Alternatively, a different configuration may be used.

A process chamber 50 is shown that can process a number of wafers W.Alternatively, a different configuration may be used. In addition, anexhaust system 65 is shown that includes a pressure controller 16.Alternatively, a different configuration may be used.

For example, a system may contain the following:

1) Gas supply system: This system can include one or more N₂ lines aswell as the required process gas lines. For example, a gas line, such asa silane gas line, can contain the following:

-   -   a) SiH₄ line with:        -   i) Check valve: HV3        -   ii) Pressure test point: PT3    -   b) N₂ bypass line with:        -   i) Check valve: HV2        -   ii) Pressure test point: PT2    -   c) Mass flow meter: MFM1    -   d) Mass flow controller: MFC5    -   e) Isolation valves: V8 and V9    -   f) Chamber isolation valve: HV7

2) Exhaust system: The exhaust system can include one or more of thefollowing:

-   -   a) Main valve: MV, and slow valves: SV and SSV    -   b) Automatic pressure controller: APC    -   c) Vacuum gauge: VG5, ˜100 Torr    -   d) Vacuum gauge: VG2, ˜1000 Torr

3) Process chamber: The process chamber can include one or more of thefollowing:

-   -   a) Vacuum gauge: VG1, 0˜10 Torr    -   b) Pirani gauge: VG3

In one embodiment, BIST rules can be created for gas supply systemcomponents, for exhaust system components, for chamber components, fortemperature control components, for wafer transfer components, and/orother system components.

FIG. 11 illustrates a simplified flow diagram of a method of monitoringa processing system in real-time using one or more process models inaccordance with embodiments of the invention. A number of process modelscan be created for a processing system that can includes temperaturecontrol components, pressure control components, gas supply components,controller components, measurement components that can include physicaland/or virtual sensors, mechanical components, computing components, orsoftware components, or combinations thereof. Procedure 1100 can startin 1110.

In 1115, one or more processes can be performed on one or more waferspositioned in a processing chamber in a processing system. In oneembodiment, the one or more wafers can be transferred into the chamberand the chamber can be sealed. In various embodiments, the one or morewafers can include a production wafer, an instrumented wafer, a testwafer, or a dummy wafer, or can be a lot that includes a combinationthereof. In some cases, a plurality of wafers may be positioned atdifferent heights in the processing chamber, and the processing chambercan be sealed. For example, a vertical boat can be used to position thewafers in a thermal processing chamber.

Prior to performing a process, pre-processing conditions can beestablished. For example, chamber pressure, chamber temperature, wafertemperature, and/or process gas conditions can be changed topre-processing before a process is performed. In some cases, thepre-processing values may be equal to operational values.

A processing system can obtain data and can use the data to determinethe operational conditions that are required before, during, and/orafter a process is performed. In addition, the data can include dynamicand/or static modeling information for predicting the performance of theprocessing system before, during, and/or after the process is performed.Furthermore, the data can include measured and/or predicted data fromprevious processes.

In addition, the data can include feedforward data, feedback data,recipe data, historical data, wafer state data, such as criticaldimension (CD) data, profile data, thickness data, uniformity data, andoptical data, such as refractive index (n) data and extinctioncoefficient (k) data. Wafer state data can also include the number oflayers, layer position, layer composition, layer uniformity, layerdensity, and layer thickness. Layers can include semiconductor material,resist material, dielectric material, and/or metallic material. Inaddition, data can comprise correction data, error data, measurementdata, or prediction data, or a combination of two or more thereof.

Referring again to FIG. 11, in 1120, the process can be monitored inreal time using at least one process model and at least one BIST rule.The process model can be created using a set of nonlinear differentialequations {dot over (x)}₁ and an output equation y₁, as follows:{dot over (x)} ₁=ƒ(x ₁ ,p ₁ ,u ₁)+w₁y ₁ =g(x ₁ ,p ₁ ,u ₁)+v ₁wherein the vector x₁ comprises a state vector, the vector pi comprisesone or more modeling parameters, the vector u₁ comprises one or moreinputs applied to the process, w₁ is a first additive white noise valuehaving a zero mean, and v₁ is a second additive white noise value havinga zero mean.

The values for the vector x₁, the vector p₁, the vector u₁, and thenoise terms w₁ and v₁ can be determined using a first set of processrecipes, a first set of component characteristics, a first set ofassumptions, a first set of operational conditions, or a first set ofBIST rules, or a combination thereof.

During various embodiments, a first process can be performed on the oneor more wafers that are positioned within the processing chamber and thepressure can be reduced in the processing chamber.

In one example, the rate of change for chamber pressure {dot over(P)}_(c) can be modeled as a function ƒ of chamber pressure (P_(c)), aprocess parameter (v) that can be related to a valve and/or pump coupledto the processing chamber, and process parameters p₁-p_(n) that can beprocess parameters other than chamber pressure P_(c), (such as gasflows), and the model can be shown as follows:{dot over (P)} _(c)=ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

A special operational condition exists when the valve is fully closed—inthis case, the pressure rise rate becomes independent of the pressurecontroller. For this condition, the chamber pressure rise rate {dot over(P)}_(c) can be:{dot over (P)} _(c)=ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v=0)

Given this model, one method for individually estimating MFC flow ratesincludes using an inverse model:p _(i)=ƒ_(i) ⁻¹({dot over (P)} _(c))

In addition, the steady-state behavior can be modeled as follows:P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

An inverse model can be used to estimate a parameter given the rest ofthe parameters, that is:p ₁ =g ₁ ⁻¹(P _(c) ,v), andv=g ₁ ⁻¹(p ₁ ,p ₂ , . . . , p _(n) ,P _(c))P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

The valve angle opening can be measured in percent, and the processingchamber pressure can be measured in mTorr. Alternatively, the openingcan be expressed as an angular position or an opening size. In addition,a pump may be used to control chamber pressure and it may becharacterized using a flow rate or a pressure difference. These modelsprovide multiple estimates of the process parameters for differentoperational conditions in which the rate of change for chamber pressurecan be used to monitor a system. For example, flow rates for processgasses and/or backside gasses may be monitored using these models. Inaddition, BIST rules can be created for the process gas supply systemand/or the backside gas system.

In a second example, the rate of change for chamber temperature {dotover (T)}_(c) can be modeled as a function ƒ of a process parameter (h)that can be related to a temperature control element coupled to theprocessing chamber, and process parameters p₁-p_(n) that can be processparameters other than chamber temperature T_(c), (such as gas flows,pressures, concentrations, etc), and the model can be shown as follows:{dot over (T)} _(c)=ƒ₂(p ₁ ,p ₂ , . . . , p _(n) ,h)

A special operational condition exists when the heater power is turnedoff—in this case, the rate of change for the chamber temperature maybecome independent of the temperature controller. For this condition,the rate of change for the chamber temperature {dot over (T)}_(c) canbe:{dot over (T)}=ƒ₂(p ₁ ,p ₂ , . . . , p _(n) ,h=0)

Given this model, one method for individually estimating chambertemperatures includes using an inverse model:p _(i)=ƒ₂ ⁻¹({dot over (T)}_(c))

In addition, the steady-state behavior can be modeled as follows:

T _(c) =g ₂(p ₁ ,p ₂ , . . . , p _(n) h)

An inverse model can be used to estimate a value for a process parametergiven the rest of the process parameters, that is:p _(i)=g₂ ⁻¹(T _(c) ,h)h=g ₂ ₂ ⁻¹(p ₁ ,p ₂ , . . . , p _(n) ,T _(c)), andT _(c) =g ₂(p ₁ ,p ₂ , . . . , p _(n) ,h)

Thus, these models provide multiple estimates of the process parametersfor different operational conditions in which the rate of change forchamber temperature can be used to monitor a system. For example, flowrates for process gasses can be monitored using these models.

In a third example, rate of change for a reactant concentration {dotover (R)} can be modeled as a function ƒ a process parameter r that isrelated to a flow control element coupled to the processing chamber, andprocess parameters p₁-p_(n) that can be process parameters other thanreactant concentration (such as gas flows, temperatures, pressures,concentrations, etc.), and the model can be shown as follows:{dot over (R)}=ƒ₃(p ₁ ,p ₂ , . . . , p _(n) , r)

A special operational condition exists when the gas valve is fullyclosed—in this case, rate of change for a reactant concentration {dotover (R)} becomes independent of the gas flow controller. For thisoperational condition, the rate of change for the reactant concentration{dot over (R)} can be:{dot over (R)}=ƒ₃(p ₁ ,p ₂ , . . . , p _(n) ,r=0)

Given this model, one method for individually estimating wafer surfacestates includes using an inverse model:p _(i)=ƒ₃ ⁻¹({dot over (R)})

In addition, the steady-state behavior can be modeled as follows:R=g ₃(p ₁ ,p ₂ , . . . , p _(n) ,r)

An inverse model can be used to estimate a parameter given the rest ofthe parameters, that is:p _(i) =g ₃ ⁻¹(R,r),r=g ₃ ⁻¹(p ₁ ,p ₂ , . . . , p _(n) ,R), andR=g ₃(p ₁ ,p ₂ , . . . , p _(n) ,r),

In a fourth example, in a single wafer system where a wafer ispositioned on a temperature controlled wafer holder, the rate of changefor wafer temperature {dot over (T)}_(w) can be modeled as a function ƒof a process parameter z that is related to a temperature controlelement coupled to a substrate holder in the processing chamber, andprocess parameters p₁-p_(n) that can be process parameters other thanwafer temperature {dot over (T)}_(w), (such as backside gas flows,temperatures, pressures, concentrations, etc.), and the model can beshown as follows:{dot over (T)} _(w)=ƒ₄(p ₁ ,p ₂ , . . . , p _(n) ,z)

A special operational condition exists when the power to a heater in thesubstrate holder is turned off—in this case, the rate of change for thewafer temperature may become independent of the heater power controller.For this condition, the rate of change for the wafer temperature {dotover (T)}_(w) can be:{dot over (T)} _(w)=ƒ₄(p ₁ ,p ₂ , . . . , p _(n) ,z=0)Given this model, one method for individually estimating wafertemperatures includes using an inverse model:p _(i) =ƒ ₃ ⁻¹({dot over (T)} _(w))In addition, the steady-state behavior can be modeled as follows:T _(w) =g ₃(p ₁ ,p ₂ , . . . , p _(n) ,z),

Given this model, one method for individually estimating backside flowrates includes using an inverse model:p _(i)=ƒ₄ ⁻¹({dot over (T)}_(w))

In addition, the steady-state behavior can be modeled as follows:T _(w) =g ₄(p ₁ ,p ₂ , . . . , p _(n) ,z),

An inverse model can be used to estimate a parameter given the rest ofthe parameters, that is:p _(i) =g ₄ ⁻¹(T _(w) ,z),z=g ₄ ⁻¹(p ₁ ,p ₂ , . . . , p _(n) ,T _(w)), andT _(w) =g ₄(p ₁ ,p ₂ , . . . , p _(n) ,z),

Thus, these models provide multiple estimates of the process parametersfor different operational conditions in which the rate of change forwafer temperature can be used to monitor a system. For example, flowrates for backside gasses can be monitored using these models. Softwarecan be used to examine the estimated parameters to generate diagnosticsbased on the operational conditions, and operational limits in the BISTtable.

In one case, a first process model can be determined for the firstprocess that relates a first rate of change for at least one parameterof a first set of first process parameters to a second set of firstprocess parameters as and/or after a first parameter in the second setis changed from a first value to a second value, wherein the second setdoes not include the at least one parameter of the first set. The firstprocess parameters are selected from the vectors x₁, p₁, and u_(i) inthe process model described above.

In one embodiment, the monitoring process can include measuring a rateof change for at least one parameter of a first set of processparameters as a first parameter in a second set of process parameters ischanged from a first value to a second value. The second set of processparameters does not include the at least one parameter of the first setof process parameters. The measured rate of change can be determined bymonitoring one or more process parameters in real-time as and/or afterthe first parameter of the second set is changed from a first value to asecond value. For example, the monitoring process may include measuringa rate of change for chamber pressure as and/or after a valve opening ischanged from a first position to a second position.

In addition, a first inverse process model can be executed for the firstprocess that relates the first measured rate of change to a value for asecond parameter in the second set of first process parameters to obtaina predicted value for the second parameter. For example, an inversemodel may relate the second parameter, such as a gas flow rate, to themeasured rate of change for chamber pressure. Alternatively, other ratesof change and other process parameters may be used.

The predicted value for the process parameter can be compared to anexpected value for the process parameter. The dynamic estimation errorcan be calculated using the difference between the predicted value forthe process parameter and the expected value for the process parameter.The expected value may be a dynamically changing value, a measuredvalue, a stored value, a historical value, a calculated value, and/or arecipe setpoint. For example, the predicted value may be a predicted gasflow rate and the expected value may be an expected gas flow rate.

In one embodiment, a first dynamic estimation error for the firstprocess can be calculated using a difference between the predicted valuefor the second parameter in the second set of first process parametersand an expected value for the second parameter, and the expected valuefor the second parameter can be determined using a process recipe, anoperational condition, or a BIST rule for the first process. Forexample, a dynamic estimation error may be calculated using thedifference between a predicted gas flow rate and an expected gas flowrate. Alternatively, the dynamic estimation error may be calculatedusing a difference between a predicted value, a measured value, acalculated value, and/or a historical value for a process parameter.

In some processing systems, a pressure control system can be coupled tothe processing chamber, and the pressure control system can include agate valve and the chamber pressure change rate can be dependent on thegate valve opening. For example, a process model may relate a rate ofchange for chamber pressure to the second set of process parameters thatdoes not include chamber pressure as and/or after a valve opening ischanged from a first position to a second position.

Alternatively, the pressure control system can include a pump and thechamber pressure change rate may be dependent on a pump speed and/orpumping volume. For example, a process model may relate a rate of changefor chamber pressure to the second set of process parameters that doesnot include chamber pressure as and/or after a pump speed and/or pumpingvolume is changed from a first value to a second value. In other cases,pump and valve parameters may be combined.

In some processing systems, a temperature control system can be coupledto the processing chamber, and the temperature control system caninclude a heater and the chamber temperature change rate can bedependent on the heater power. For example, a process model may relate arate of change for chamber temperature to the second set of processparameters that does not include chamber temperature as and/or after aheater power is changed from a first power level to a second powerlevel. In addition, an inverse model may relate a reaction rate to themeasured rate of change for chamber temperature, and a dynamicestimation error may be calculated using the difference between thepredicted value for a reaction rate and the expected value for thereaction rate.

In some processing systems, a temperature control system can be coupledto a wafer holder in a processing chamber, and the temperature controlsystem can include a wafer heater in the wafer holder and the wafertemperature change rate can be dependent on the heater power provided tothe wafer heater. For example, a process model may relate a rate ofchange for wafer temperature to the second set of process parametersthat does not include wafer temperature as and/or after the wafer heaterpower is changed from a first power level to a second power level. Inaddition, an inverse model may relate a flow rate for a backside gas tothe measured rate of change for wafer temperature, and a dynamicestimation error may be calculated using the difference between thepredicted value for a flow rate for a backside gas and the expectedvalue for flow rate for a backside gas.

Referring again to FIG. 11, in 1125, a query can be performed in whichthe dynamic estimation error is compared to an operational limitestablished for the process. In one embodiment, the first dynamicestimation error for the first process can be compared to an operationallimit established for the first process; the first process (waferprocessing) can continue when the first dynamic estimation error iswithin the operational limit; and the first process can be examined whenthe first dynamic estimation error is not within the operational limit.In addition, the operational limit is established by a thresholddetermined for one or more BIST rules in a BIST table for the firstprocess. Alternatively, the operational limit may be established by athreshold determined for one or more rules in an operational conditionstable for the first process or by a process recipe table.

Procedure 1100 can branch to 1150 and continue when the dynamicestimation error is within the operational limit established for theprocess. The difference between the dynamic estimation error for theprocess and the operational limit established for the process can bemonitored to predict potential problems. For example, process drift maybe identified, degrading components may be identified, and/or cleaningtimes may be identified. Procedure 1100 can branch to 1130, andprocedure can continue when the dynamic estimation error is not withinthe operational limit established for the process. BIST rules, processresults data, and operational conditions data can be stored in the BISTtable before, during, and/or after the process is performed.

In 1130, a query can be performed in which the dynamic estimation erroris compared to a warning limit established for one or more BIST rules inthe BIST table for the process. Alternatively, the warning limit may beestablished by a threshold determined for one or more rules in anoperational conditions table for the first process or by a processrecipe table.

Procedure 1100 can branch to 1150 and continue when the dynamicestimation error is within the warning limit established for theprocess. The difference between the dynamic estimation error for theprocess and the warning limit can be monitored to predict potentialproblems. For example, process drift may be identified,degrading/failing components may be identified, and/or cleaning timesmay be identified. Procedure 1100 can branch to 1135, and can continuewhen the dynamic estimation error is not within the warning limitestablished for the process. A warning message can be sent when dynamicestimation error is within and/or approaching the warning limit.Alternatively, a process may be paused or stopped when a warning messageis sent and operator intervention may be required. A fault message canbe sent when dynamic estimation error is not within and/or approachingthe warning limit.

In 1135, a query can be performed to determine if the monitoringprocedure requires modification. The query can be performed to determineif a new process model, a new BIST rule, a new process recipe, or amaintenance procedure, or a combination thereof, is required when thedynamic estimation error is not within the warning limit established forthe process. During a monitoring procedure, a controller can be used todetermine if the process being performed is a new process or isassociated with a new BIST rule. Procedure 1100 can branch to 1140 whenthe monitoring procedure requires modification, and procedure 1100 canbranch to 1150 when a modification is not required.

In 1140, the monitoring procedure can be modified. During modification,a new process model for the process can be determined when a new processmodel is required, and the new process model relates a new first rate ofchange for at least one new parameter of a new first set of processparameters to a new second set of process parameters as and/or after anew first parameter in the new second set is changed from a new firstvalue to a new second value. The new second set does not include the atleast one new parameter of the new first set, and the wafer processingcan continue using the new process model.

In addition, a new BIST rule can be created for the process when a newBIST rule is required, the new BIST rule having new operational andwarning limits, new tolerance values, and new messages and being basedon at least one pre-existing BIST rule created for the process. The newBIST rule with the new operational limit and the new tolerance valuescan be entered into a BIST table, and wafer processing can continue.

Furthermore, a new process recipe can be established for the processwhen a new process recipe is required, and the new process recipe canhave new process parameters and a new BIST rule associated therewith.The new process parameters can have values within and/or outside ofnormal production limits. During normal production processing, the newprocess parameters can have values within the normal production limits.During non-production processing, the new process parameters can havevalues outside the normal production limits. The new BIST rule and newprocess recipe can be entered into a BIST table when the new BIST ruleis not in the BIST table, and wafer processing can continue using thenew process recipe.

The monitoring procedure can be paused or stopped when the procedurecannot be modified, that is when a new BIST rule cannot be created, or anew process recipe cannot be established, or a maintenance procedure isrequired. Procedure 1100 can branch to 1145 when a maintenance procedureis required.

In one embodiment, when the dynamic estimation error is not within thewarning limit, the real-time dynamic model, the predicted parametervalue, the measured rate of change, and/or the dynamic estimation errorcan be examined, and a new BIST rule or process recipe with new valuesbased on the current and/or pre-existing values can be established. Inaddition, the new BIST rule and or process recipe with new operationaland warning limits and new tolerance values can be stored, and procedure1100 can continue.

Alternatively, the monitoring software may need data from anothercontroller (host) and/or input from a user to determine when to create anew BIST rule. In addition, the rate of change for a process parameterand/or a process drift value for the process can be monitored, and oneor more BIST rules can be created and/or used when a process parameterand/or a process drift value for the process approaches an operationaland/or warning limit. For example, special BIST rules may be establishedto monitor process drift, and these special BIST rules may be used todetermine when a cleaning and/or maintenance procedure should beperformed.

In 1145, a maintenance procedure can be performed. On or more BIST rulescan be used to determine the type of maintenance that is required. Whena maintenance procedure is completed, procedure 1100 can branch to 1165.In addition, BIST rules may be used during the maintenance procedure.

In 1150, a query can be performed to determine when an additionalprocess is required. When another process is required, procedure 1100can branch to 1115, and when another process is not required, procedure1100 can branch to 1155. When the process is performed multiple timesand/or multiple processes are performed, one or more different modelscan be executed and one or more different BIST rules, process recipes,operational conditions, and/or sets of process parameters can be used.

In 1155, a query can be performed to determine when a different processis required. When a different process is required, procedure 1100 canbranch to 1160, and when a different process is not required, procedure1100 can branch to 1165.

In 1160, one or more different processes can be performed and monitoringprocedures as described herein may be used. When a different process isrequired, one or more wafers can be transferred to another processingsystem, or one or more of the wafers can be transferred to a measurementsystem.

In 1165, procedure 1100 can end. When procedure 1100 ends, one or morewafers can be removed from the processing chamber, transferred to astorage location, and/or transferred to a measurement tool.

When a monitoring procedure, such as procedure 1100, is performed, thefirst parameter in the second set of first process parameters can bechanged using a series of steps; the process model can be determinedusing the series of steps; the measured rate of change can be determinedusing the series of steps; the inverse process model can be executedusing the series of steps; and the dynamic estimation error can becalculated using the series of steps.

In other embodiments, when a monitoring procedure, such as procedure1100, is performed, a wafer can be divided into a plurality ofmeasurement zones; the process model can be determined using theplurality of measurement zones; the measured rate of change can bedetermined using the plurality of measurement zones; the inverse processmodel can be executed using the plurality of measurement zones; and thedynamic estimation error can be calculated using the plurality ofmeasurement zones.

In other embodiments, when a monitoring procedure, such as procedure1100, is performed, the processing chamber can be divided into aplurality of measurement zones; the process model can be determinedusing the plurality of measurement zones; the measured rate of changecan be determined using the plurality of measurement zones; the inverseprocess model can be executed using the plurality of measurement zones;and the dynamic estimation error can be calculated using the pluralityof measurement zones.

In additional embodiments, when a monitoring procedure, such asprocedure 1100, is performed, a plurality of temperature control zonescan be established in the processing chamber; the thermal interactionbetween the temperature control zones can be modeled; and the thermalinteraction model can be used to determine the process model and/or theinverse process model. In addition, a plurality of gas flow controlzones can be established in the processing chamber; the flow interactionbetween the gas flow control zones can be modeled; and the flowinteraction model can be used to determine the process model and/or theinverse process model.

In other additional embodiments, when a monitoring procedure, such asprocedure 1100, is performed, the thermal interaction between the one ormore wafers and a processing space within the processing chamber can bemodeled; and this thermal interaction model can be used to determine theprocess model and/or the inverse process model.

Furthermore, a wafer curvature model may be created when one or morecurved wafers are being processed; and the wafer curvature model may beincorporated into the process model and/or the inverse process model.

Before, during, and/or after a monitoring procedure is performed,historical data can be obtained, and the historical data can be used todetermine the process to perform, the process recipe to use, the BISTtables to use, and/or the process models to use. In addition, waferstate data can be obtained, and the wafer state can be used to determinethe process to perform, the process recipe to use, the BIST tables touse, and/or the process models to use.

A procedure, such as illustrated in FIG. 11, can be used with a thermalprocessing system, a MLD system, an etching system, a deposition system,a plating system, a polishing system, an implant system, a developingsystem, or a transfer system, or a combination of two or more thereof.In addition, the processes performed can include a MLD process, athermal process, an etching process, a deposition process, a platingprocess, a polishing process, an implant process, a developing process,or a transfer process, or a combination of two or more thereof.

In one embodiment, a procedure, such as illustrated in FIG. 11, can beused with a deposition procedure that includes using a first precursorprocess, a first purging process, a second precursor process, and asecond purging process. When creating process models for processingsystems operating at low pressures and using process recipes thatinclude injecting a process gas, such as a precursor-containing gas or apurging gas, into the processing chamber, one or more models can becreated that relate a gas flow rate (GFR) for a process gas to a rate ofchange for pressure (RCP) within the processing chamber and/or withinone or more control zones in the processing chamber. For example, a rateof change can be expressed as a positive or negative number.Alternatively, a pressure rise rate (PRR) may be used.

For example, a simplified model of a processing chamber can be createdthat relates a first process parameter, such as Gas Flow Rate (GFR), tothe rate of change of a second process parameter, such as a Rate ofChange of Pressure (RCP). Then, for any given process recipe step whileand/or after a gate valve position is changed and a process gas flow isintroduced, a Measured Rate of Change of Pressure (MRCP) can be obtainedby monitoring the real-time process parameters. Next, using the MRCP andone or more process models, a Predicted Gas Flow Rate (PGFR) can becalculated. Then, the PGFR can be compared to the Expected Gas Flow Rate(EGFR)—an expected gas flow rate for a process gas can be a setpoint inthe recipe. A dynamic estimation error can be calculated using thedifference between the predicted value PGFR and expected value EGFR. Thedynamic estimation error can be compared to a limit established for thecurrent operating condition. A process can continue when the dynamicestimation error is within the operational limit, and the operationallimit can be established by a BIST rule.

In addition, when the dynamic estimation error is not within theoperational limit, the dynamic estimation error can be compared to awarning limit for the process established by one or more BIST rules inthe BIST table for the process, and a warning message can be sentidentifying a potential problem with the process and/or the MLD systemand the process continued when the first dynamic estimation error iswithin the warning limit, or a fault message can be sent identifying aknown problem with the process and/or the MFC system and the processstopped when the dynamic estimation error is not within the warninglimit. The process and/or processing system can be examined further whenthe dynamic estimation error is not within the operational limitestablished for the process. Alternatively, a dynamic estimation errormay be determined using a calculated value, a measured value, ahistorical value, and/or an expected value.

For example, another simplified model of a process may be created thatrelates a first process parameter, such as Wafer Temperature (WT), tothe rate of change of a second process parameter, such as a ChamberTemperature Rate of Change (CTRC). Then, for any given process recipestep while and/or after a power level is changed, a Measured ChamberTemperature Rate of Change (MCTRC) can be obtained by monitoring thereal-time process parameters. Next, using the MCTRC and one or moreprocess models, a Predicted Wafer Temperature (PWT) can be calculated.Then, the PWT can be compared to the Expected Wafer Temperature(EWT)—this expected wafer temperature can be the setpoint in the recipe.A dynamic estimation error can be calculated using the differencebetween the predicted value PWT and expected value EWT. The dynamicestimation error can be compared to a limit established for the currentoperating condition. Alternatively, a dynamic estimation error may bedetermined using a calculated value, a measured value, a historicalvalue, and/or an expected value.

In addition, another simplified model of a process can be created thatrelates a first process parameter, such as Backside Gas Flow Rate(BGFR), to the rate of change of a second process parameter, such as aWafer Temperature Rate of Change (WTRC). Then, for any given processrecipe step while and/or after wafer heater power is changed and abackside gas is introduced, a Measured Wafer Temperature Rate of Change(MWTRC) can be obtained by monitoring the real-time process parameters.Next, using the MWTRC and one or more process models, a PredictedBackside Gas Flow Rate (PBGFR) can be calculated. Then, the PBGFR can becompared to the Expected Backside Gas Flow Rate (EBGFR)—this expectedbackside gas flow rate can be the setpoint in the recipe. A dynamicestimation error can be calculated using the difference between thepredicted value PBGFR and expected value EBGFR. The dynamic estimationerror can be compared to a limit established for the current operatingcondition. Alternatively, a dynamic estimation error may be determinedusing a calculated value, a measured value, a historical value, and/oran expected value.

For example, another simplified model of a process may be created thatrelates a first process parameter, such as reactant concentration (RC),to the rate of change of a second process parameter, such as a rate ofchange for the gas flow rate (RCGFR). Then, for any given process recipestep while and/or after an MFC is changed and a reactant gas flow isintroduced, a Measured Rate of Change for a Gas Flow Rate (MRCGFR) canbe obtained by monitoring the real-time process parameters. Next, usingthe MRCGFR and one or more models, a Predicted Reactant Concentration(PRC) can be calculated. Then, the PRC can be compared to the ExpectedReactant Concentration (ERC)—this expected reactant concentration can bea setpoint in the recipe. A dynamic estimation error can be calculatedusing the difference between the predicted value PRC and expected valueERC. The dynamic estimation error can be compared to a limit establishedfor the current operating condition. Alternatively, a dynamic estimationerror may be determined using a calculated value, a measured value, ahistorical value, and/or an expected value.

In addition, another simplified model of a process can be created thatrelates a first process parameter, such as Backside Gas Flow Rate(BGFR), to the rate of change of a second process parameter, such as aWafer Temperature Rate of Change (WTRC). Then, for any given processrecipe step while and/or after a “backside” MFC is changed and abackside gas is introduced, a Measured Wafer Temperature Rate of Change(MWTRC) can be obtained by monitoring the real-time process parameters.Next, using the MWTRC and the model described above, a PredictedBackside Gas Flow Rate (PBGFR) can be calculated. Then, the PBGFR can becompared to the Expected Backside Gas Flow Rate (EBGFR)—this expectedbackside gas flow rate can be the setpoint in the recipe. A dynamicestimation error can be calculated using the difference between thepredicted value PBGFR and expected value EBGFR. The dynamic estimationerror can be compared to a limit established for the current operatingcondition. Alternatively, a dynamic estimation error may be determinedusing a calculated value, a measured value, a historical value, and/oran expected value.

Alternatively, one or more models may be created that can relate a rateof change for at least one parameter of a first set of processparameters to a process parameter value for an “un-measurable” processparameter that is not included in the first set of process parameters.For example, the monitoring process may include determining a measuredpressure rise rate (MPRR) by monitoring one or more process parametersas the process gas is flowed into the processing chamber, calculating apredicted value for an “un-measurable” process parameter (PUPP) usingthe process model, and comparing the predicted/calculated (PUPP) to anexpected value for the “un-measurable” process parameter (EUPP), wherethe (EUPP) has been established by the process recipe value.

In addition, one or more models may be created that relate a gas flowrate (GFR) for a process gas to a rise rate value for an “un-measurable”process parameter (MURR) that may be estimated using virtual sensorsconfigured within the processing chamber and/or within one or morecontrol zones in the processing chamber. The monitoring process caninclude determining a rise rate value for an “un-measurable” (MURR) byusing one or more virtual sensors to estimate one or more“un-measurable” process parameters as the process gas is flowed into theprocessing chamber, calculating a predicted gas flow rate (PGFR) using aprocess model, and comparing the predicted/calculated (PGFR) to anexpected gas flow rate (EGFR), where the EGFR has been established by afixed and/or intelligent set point in the process recipe. Techniques forestablishing virtual sensors and intelligent set points are taught inco-pending U.S. patent application Ser. Nos. 11/043,199 and 11/043,459(Attorney Docket Nos. TPS-005 and TPS-009), each entitled “METHOD ANDAPPARATUS FOR MONOLAYER DEPOSITION” and each filed on Jan. 26, 2005,both of which are incorporated herein by reference in their entirety.

The simplified models are shown herein for the illustrative purposes andare not intended to limit the scope of the invention. For example, thevariables can be replaced with vectors, multivariable functions, andmultivariable equations.

FIG. 12 illustrates a simplified flow diagram of a method of monitoringa monolayer deposition (MLD) system in real-time using one or moreprocess models in accordance with embodiments of the invention.Monolayer deposition techniques are also taught in U.S. patentapplication Ser. Nos. 11/043,199 and 11/043,459, referred to above.

A number of process models and operating conditions can be created for aprocessing system that can include temperature control components, thepressure control components, gas supply components, mechanicalcomponents, computing components, or software components, orcombinations thereof.

The MLD procedure 1200 can start in 1205 in which pre-processingconditions can be established. For example, the processing chamber canbe sealed, and the chamber pressure, chamber temperature, wafertemperature, and/or process gas conditions can be changed to operationalor pre-operational values before a process is performed.

A processing system can obtain data and use the data to establish one ormore recipes to use before, during, and/or after a process is performed.In addition, the data can include dynamic and/or static modelinginformation for predicting the performance of the processing systembefore, during, and/or after the process is performed. Furthermore, thedata can include measured and/or predicted data from previous MLDprocesses.

In addition, the data can include recipe data, historical data, waferdata, such as critical dimension (CD) data, profile data, thicknessdata, uniformity data, and optical data, such as refractive index (n)data and extinction coefficient (k) data. Wafer data can also includethe number of layers, layer position, layer composition, layeruniformity, layer density, and layer thickness. Layers can includesemiconductor material, resist material, dielectric material, and/ormetallic material. In addition, data can comprise correction data, errordata, measurement data, or historical data, or a combination of two ormore thereof.

In task 1210, a precursor process can be performed on a plurality ofwafers positioned in the processing chamber in a processing system. Inone embodiment, the wafers can be positioned at different heights in a“batch-type” processing chamber. For example, a vertical boat can beused to position the wafers in a batch-processing chamber. In variousembodiments, the wafers can include production wafers, instrumentedwafers, test wafers, or dummy wafers, or combinations thereof. Inaddition, the thermal processing chamber can include a plurality ofcontrol zones and the precursor processing models, the operatingconditions, and/or precursor process recipes can be different in one ormore of the plurality of control zones.

When a first precursor process is performed, a firstprecursor-containing gas can be flowed into the thermal processingchamber. The first precursor-containing gas can include a firstprecursor, a first carrier gas, and/or an inert gas. When a secondprecursor process is performed, a second precursor-containing gas can beflowed into the thermal processing chamber. The secondprecursor-containing gas can include a second precursor, a secondcarrier gas, and/or an inert gas.

When a first precursor process is being performed, one or more of theprocess parameters can be changed from a first value to a second value,and one or more real-time dynamic process models can be created that canbe used to predict the system's response.

When a precursor process is performed, a precursor process (first and/orsecond) can be monitored using a first set of nonlinear differentialequations {dot over (x)}₁ and a first output equation y₁, wherein{dot over (x)} ₁=ƒ(x ₁ ,p ₁ ,u ₁)y ₁ =g(x ₁ ,p ₁ ,u ₁)and x₁, p₁, and u₁ are precursor process parameters in which the firstvector x₁ comprises a first state vector for the precursor process, thefirst vector p₁ comprises one or more modeling parameters for theprecursor process, and the vector u₁ comprises one or more inputsapplied to the precursor process.

A dynamic estimation error for a precursor process (first and/orsecond), and the dynamic estimation error can be compared to anoperational limit established by one or more BIST rules in the BISTtable for the precursor process. The precursor process can continue whenthe dynamic estimation error is within the operational limit; and thedynamic estimation error can be compared to a warning limit establishedfor the precursor process when the dynamic estimation error is notwithin the operational limit.

When the dynamic estimation error is within the warning limit, a warningmessage can be sent that identifies a potential problem with theprecursor process and/or the MLD system, and the precursor process cancontinue. The BIST rule that is presently being used in the calculationprocess can be used to identify the potential problem with the precursorprocess and/or the MLD system.

When the dynamic estimation error is not within the warning limit, afault message can be sent that identifies a known problem with theprecursor process and/or the MLD system and the precursor process can bestopped. The BIST rule that is presently being used in the calculationprocess can be used to identify the known problem with the precursorprocess and/or the MLD system.

When the dynamic estimation error is being calculated, a precursorprocess model can be determined for the precursor process that relates afirst rate of change for at least one parameter of a first set ofprecursor process parameters to a second set of the precursor processparameters as and/or after a first parameter in the second set ischanged from a first value to a second value, and the second set doesnot include the at least one parameter of the first set.

In a first example, a precursor process model may relate a rate ofchange for chamber pressure to the second set of precursor processparameters that does not include chamber pressure as and/or after apressure control parameter (gate valve parameter and/or pump parameter)is changed from a first value to a second value.

In second example, a precursor process model may relate a chamberchemistry state (a reactant concentration for precursor molecules) inthe thermal processing chamber to a rate of change for chamber pressurein the thermal processing chamber as and/or after a pressure controlparameter (gate valve parameter and/or pump parameter) is changed from afirst value to a second value.

In a third example, a precursor process model may relate a chamberchemistry state (a reactant concentration for the first precursormolecules) in the thermal processing chamber to a rate of change for theflow rate for a process gas, such as a precursor-containing gas, intothe thermal processing chamber as and/or after a gas system flow controlparameter (mass flow control valve position) is changed from a firstvalue to a second value.

In a fourth example, a precursor process model may relate a substratetemperature for a substrate in the thermal processing chamber to a rateof change for the temperature in the thermal processing chamber asand/or after a temperature control system parameter (a heater power) ischanged from a first power level to a second power level.

Alternatively, other rates of change and other process parameters may beused when developing the models and BIST rules.

Next, a first measured rate of change for the at least one parameter ofthe first set of the precursor process parameters can be determined inreal time as and/or after the first parameter in the second set of firstprecursor process parameters is changed from the first value to thesecond value. The measured rate of change can be determined bymonitoring one or more precursor process parameters in real-time asand/or after the first parameter in the second set is changed from afirst value to a second value.

In one example, a measured rate of change for chamber pressure can bedetermined, and the measured rate of change for chamber pressuredetermined as and/or after the pressure control parameter (gate valveparameter and/or pump parameter) is changed from the first value to thesecond value.

In a second example, a measured rate of change for the flow rate for aprocess gas, such as a precursor-containing gas, into the thermalprocessing chamber, and the measured rate of change for the flow ratefor the process gas is determined as and/or after a gas system flowcontrol parameter (mass flow control valve position) is changed from afirst value to a second value.

In a third example, a measured rate of change for the chambertemperature can be determined, and the measured rate of change for thechamber temperature is determined as and/or after a temperature controlsystem parameter (heater power) is changed from a first power level to asecond power level.

In a fourth example, a measured rate of change for the chamber chemistrycan be determined, and the measured rate of change for the chamberchemistry is determined as and/or after a system parameter is changedfrom a first value to a second value.

In other examples, a measured rate of change for a deposited layer, anetched layer, a saturation state, or a contamination state can bedetermined.

Then, an inverse precursor process model for the precursor process canbe executed that relates the first measured rate of change to a valuefor a second parameter in the second set of the precursor processparameters to obtain a predicted value for the second parameter.

In one example, an inverse model may relate a process gas flow rate, toa measured rate of change for chamber pressure. In a second example, aninverse model may relate a chamber chemistry state (a reactantconcentration for the precursor molecules) in the thermal processingchamber to a measured rate of change for chamber pressure. In a thirdexample, an inverse model may relate a chamber chemistry state (areactant concentration for the precursor molecules) in the thermalprocessing chamber to a measured rate of change for a flow rate for aprocess gas. In a fourth example, an inverse model may relate awafer/substrate temperature to a measured rate of change for chambertemperature and/or substrate holder temperature. In other examples, aninverse model may relate a process and/or system parameter to a measuredrate of change for a deposited layer, an etched layer, a saturationstate, or a contamination state. Alternatively, other rates of changeand other process parameters may be used.

Finally, the dynamic estimation error for the precursor process can becalculated using a difference between the predicted value for the secondparameter in the second set of the precursor process parameters and anexpected value for the second parameter, and the expected value for thesecond parameter can be determined using a BIST rule for the precursorprocess. The expected value may be a dynamically changing value, ameasured value, a stored value, a calculated value, and/or a recipesetpoint. Alternatively, the dynamic estimation error may be calculatedusing a difference between a predicted value, a measured value, acalculated value, and/or historical value for one or more processparameters.

In one example, the predicted value may be a predicted process gas flowrate and the expected value may be an expected process gas flow rate,and the process gas may include a precursor. In a second example, thepredicted value may be a predicted chamber chemistry state and theexpected value may be an expected chamber chemistry state. In otherexamples, the predicted and expected values may be depositionthicknesses, etching dimensions, saturation state values, orcontamination state values.

When creating process models for an MLD procedure being performed at lowpressures and using process recipes that include injecting aprecursor-containing gas into a thermal processing chamber that caninclude a plurality of injection/control zones, one or more models canbe created that relate a gas flow rate (GFR) for a process gas, such asa precursor-containing gas, to a rate of change for pressure (RCP)within the processing chamber and/or within one or moreinjection/control zones in the processing chamber. For example, a rateof change can be expressed as a positive or negative number.Alternatively, a pressure rise rate (PRR) may be used.

For example, a simplified model of a precursor process can be createdthat relates a first process parameter, such as Precursor-Containing GasFlow Rate (PCGFR), to the rate of change of a second process parameter,such as a Rate of Change of Pressure (RCP). Then, for any given processrecipe step while and/or after a valve position is changed and a processgas is introduced, a Measured Rate of Change of Pressure (MRCP) can beobtained by monitoring the real-time process parameters during theprecursor process. Next, using the MRCP and one or more models, aPredicted Precursor-Containing Gas Flow Rate (PPCGFR) can be calculated.Then, the PPCGFR can be compared to an Expected Precursor-containing GasFlow Rate (EPCGFR)—the expected gas flow rate can be associated with theprecursor-containing gas and can be established by a setpoint in theprecursor process recipe. A precursor process dynamic estimation errorcan be calculated using the difference between the predicted valuePPCGFR and expected value EPCGFR. The precursor process dynamicestimation error can be compared to limits established for the currentoperating condition. Alternatively, other process parameters and otherrates of change may be used.

Referring again to FIG. 12, in 1215, a query can be performed todetermine whether to continue the precursor process. When the precursorprocess is operating within limits established for the precursorprocess, procedure 1200 can branch to 1230. When the precursor processis not operating within limits established for the precursor process,procedure 1200 can branch to 1220.

In one embodiment, the precursor process dynamic estimation error iscompared to an operational limit established for one or more BIST rulesin the BIST table for the precursor process. The precursor process cancontinue when the precursor process dynamic estimation error is withinthe operational limit. When creating and or verifying BIST rules, aprecursor process may be continued, paused, or stopped when theprecursor process dynamic estimation error is not within the operationallimit. For example, operator and/or host intervention may be required.

In addition, the precursor process dynamic estimation error can also becompared to a warning limit established for one or more BIST rules inthe BIST table for the precursor process. The precursor process can becontinued when the precursor process dynamic estimation error is withinthe warning limit. The precursor process can be paused and/or stoppedwhen the precursor process dynamic estimation error is not within thewarning limit.

When the precursor process dynamic estimation error is not with theoperational limit, the precursor process dynamic estimation error canthen be compared to the warning limit for the precursor process; awarning message identifying a potential problem with the precursorprocess and/or the MLD system can be sent and the precursor process canbe continued when the precursor process dynamic estimation error iswithin the warning limit.

When the precursor process dynamic estimation error is not with thewarning limit, a fault message identifying a known problem with theprecursor process and/or the MLD system can be sent and the precursorprocess can be stopped.

In various embodiments, warning messages can be sent that identifypotential problems with the precursor process, the thermal processingchamber, the pressure control system coupled to the thermal processingchamber, the gas supply system coupled to the thermal processingchamber, the temperature control system coupled to the thermalprocessing chamber, the control system coupled to the thermal processingchamber, or a combination thereof.

In addition, fault messages can be sent that identify known problemswith the precursor process, the thermal processing chamber, the pressurecontrol system coupled to the thermal processing chamber, the gas supplysystem coupled to the thermal processing chamber, the temperaturecontrol system coupled to the thermal processing chamber, the controlsystem coupled to the thermal processing chamber, or a combinationthereof.

For example, BIST rules may be used for chamber components, temperaturecontrol elements, pressure control components, gas system components,and/or controller components.

In addition, the rate of change for a precursor process parameter and/orthe process drift value for the precursor process can be monitored, andone or more notification messages can be sent when a precursor processparameter and/or the process drift value for the precursor process areapproaching an operational and/or warning limit.

Referring again to FIG. 12, in 1220, a query can be performed todetermine when to modify the monitoring process for the precursorprocess. When the precursor process dynamic estimation error is notwithin the warning limit established for the precursor process, thecontroller can determine if a new precursor process model, a new BISTrule, or a new precursor process recipe, or a maintenance procedure, ora combination thereof is required. During a monitoring procedure, acontroller can be used to determine if the precursor process currentlybeing performed is a new process or should be associated with a new BISTrule. Procedure 1200 can branch to 1225, when a procedure modificationcan be made. Procedure 1200 can branch to 1230, when a proceduremodification cannot be made.

In 1225, the monitoring procedure can be modified. For example, a newBIST rule can be created for the precursor process when a new BIST ruleis required, the new BIST rule having new operational and warninglimits, new tolerance values, and new messages and being based on atleast one pre-existing BIST rule created for the process. The new BISTrule with the new operational and warning limits and the new tolerancevalues can be entered into a BIST table, and wafer processing cancontinue. A new process recipe can be established for the precursorprocess when a new process recipe is required, the new process recipecan have new precursor process parameters and a new BIST rule associatedtherewith. The new precursor process parameters can have values withinand/or outside of normal production limits. During normal productionprocessing, the new precursor process parameters can have values withinthe normal production limits. During non-production processing, the newprecursor process parameters can have values outside the normalproduction limits. The new BIST rule and new process recipe can beentered into a BIST table when the new BIST rule is not in the BISTtable, and wafer processing can continue using the new process recipe.In addition, a new precursor process model can be established.

The precursor process can be paused or stopped when the monitoringprocedure cannot be modified or a maintenance procedure is required.

Alternatively, the controller (monitoring software) may need data fromanother controller (host) and/or input from a user to determine when tomodify the monitoring procedure for a precursor process. In addition,the rate of change for a process parameter and/or a process drift valuefor the precursor process can be monitored, and one or more notificationmessages can be sent when a process parameter and/or the process driftvalue for the precursor process approach an operational and/or warninglimit.

In 1230, a query can be performed to determine when another precursorprocess is required. When another precursor process is required,procedure 1200 can branch to 1210, and when another precursor process isnot required, procedure 1200 can branch to 1235. When the precursorprocess is performed multiple times and/or multiple precursor processesare performed, one or more different precursor process models can beexecuted and one or more different precursor process recipes may beused.

During a precursor process, one or more reactants can be used andreactant/precursor molecules (R_(A) and R_(B)), can react with thesurface until the surface is saturated. For example, precursor processconditions can be chosen to stop a process step when the surface iscompletely saturated. Monolayer deposition processes sometimes use theself-limiting surface saturation aspect to control the filmcharacteristics. Alternatively, precursor processes may be made longerin order to ensure that the surface is saturated to slightlyover-saturated with precursor molecules. In some cases, the processresults can be relatively independent of slight variations in the amountof precursor supplied to the surface.

In one embodiment, during a MLD procedure, a first precursor process canbe performed that is followed by a first purging process, then a secondprecursor process can be performed that is followed by a second purgingprocess. When a first precursor process is performed, a firstprecursor-containing gas can be introduced into the processing chamber,and the plurality of wafers can be exposed to a first reactant speciescontained in the first precursor-containing gas. During the firstprecursor process, a uniform film of R_(A) molecules can be depositedonto the surfaces of the plurality of wafers. For example, surfacesaturation states can be monitored, and a physical and/or virtual sensorcan be used to determine when the surface saturation state(reactant/precursor concentration) has reached a desired value. Duringthe second precursor process, a uniform film of R_(B) molecules can bedeposited onto the layer of R_(A) molecules on the surfaces of theplurality of wafers. For example, surface reaction states can bemonitored, and a physical and/or virtual sensor can be used to determinewhen the reactant state (reacted molecule concentration) has reached adesired value.

The operational conditions for a precursor process can include: limitsfor the flow rate for the precursor-containing gas; concentration valuesfor one or more first reactant (R_(A))species (precursor molecules);limits and models for the flow between the wafers; limits for aresidence time for the first reactant species (precursor molecules);models and limits for determining a reactant species (precursormolecules) concentration for one or more surface saturation zones; andmodels and limits for determining a chemisorption rate for one or moresurface saturation zones. For example, a self-limiting reaction, such asa chemisorption reaction may be determined by a saturation time and maybe independent of the reactant exposure time after saturation.

In alternate embodiments, the BIST rules may include intelligent(time-varying) set points and/or virtual sensors.

In 1235, a query can be performed to determine whether a purging processis required. When a purging process is required, procedure 1200 canbranch to 1240, and when a purging process is not required, procedure1200 can branch to 1265.

In 1240, a purging process can be performed on the wafer(s) positionedin the processing chamber in a processing system. In one embodiment, anumber of wafers can be positioned at different heights in theprocessing chamber. In addition, the thermal processing chamber caninclude a plurality of control zones and the purging processing models,the operating conditions, and/or purging process recipes can bedifferent in one or more of the plurality of control zones. The purgingprocess can be monitored using a purging process model. Alternatively,the purging process does not require monitoring.

When monitoring is required, a purging process model can be createdusing a second set of nonlinear differential equations {dot over (x)}₂and a second output equation y₂, where{dot over (x)} ₂=ƒ(x ₂ ,p ₂ ,u ₂)y ₂ =g(x ₂ ,p ₂ ,u ₂)and the vector x₂ comprises a state vector for the purging process, thevector p₂ comprises one or more modeling parameters for the purgingprocess, the vector u₂ comprises one or more inputs applied to thepurging process. Alternatively, one or more additive white noise termshaving a zero mean may be incorporated into one or more of theequations.

A dynamic estimation error for a purging process (first and/or second),and the dynamic estimation error can be compared to an operational limitestablished by one or more BIST rules in the BIST table for the purgingprocess. The purging process can continue when the dynamic estimationerror is within the operational limit; and the dynamic estimation errorcan be compared to a warning limit established for the purging processwhen the dynamic estimation error is not within the operational limit.

When the dynamic estimation error is within the warning limit, a warningmessage can be sent that identifies a potential problem with the purgingprocess and/or the MLD system, and the purging process can continue. TheBIST rule that is presently being used in the calculation process can beused to identify the potential problem with the purging process and/orthe MLD system.

When the dynamic estimation error is not within the warning limit, afault message can be sent that identifies a known problem with thepurging process and/or the MLD system and the purging process can bestopped, The BIST rule that is presently being used in the calculationprocess can be used to identify the known problem with the purgingprocess and/or the MLD system.

When the dynamic estimation error is being calculated, a purging processmodel can be determined for the purging process that relates a firstrate of change for at least one parameter of a first set of purgingprocess parameters to a second set of the purging process parameters asand/or after a first parameter in the second set is changed from a firstvalue to a second value, and the second set does not include the atleast one parameter of the first set.

In a first example, a purging process model may relate a rate of changefor chamber pressure to the second set of purging process parametersthat does not include chamber pressure as and/or after a pressurecontrol parameter (gate valve parameter and/or pump parameter) ischanged from a first value to a second value.

In second example, a purging process model may relate a chamberchemistry state (a reactant concentration for precursor molecules) inthe thermal processing chamber to a rate of change for chamber pressurein the thermal processing chamber as and/or after a pressure controlparameter (gate valve parameter and/or pump parameter) is changed from afirst value to a second value,

In a third example, a purging process model may relate a chamberchemistry state (a reactant concentration for the first precursormolecules) in the thermal processing chamber to a rate of change for theflow rate for a process gas, such as a precursor-containing gas, intothe thermal processing chamber as and/or after a gas system flow controlparameter (mass flow control valve position) is changed from a firstvalue to a second value.

In a fourth example, a purging process model may relate a substratetemperature for a substrate in the thermal processing chamber to a rateof change for the temperature in the thermal processing chamber asand/or after a temperature control system parameter (a heater power) ischanged from a first power level to a second power level.

Alternatively, other rates of change and other process parameters may beused when developing the models and BIST rules.

Next, a first measured rate of change for the at least one parameter ofthe first set of the purging process parameters can be determined inreal time as and/or after the first parameter in the second set of firstpurging process parameters is changed from the first value to the secondvalue. The measured rate of change can be determined by monitoring oneor more purging process parameters in real-time as and/or after thefirst parameter in the second set is changed from a first value to asecond value.

In one example, a measured rate of change for chamber pressure can bedetermined, and the measured rate of change for chamber pressuredetermined as and/or after the pressure control parameter (gate valveparameter and/or pump parameter) is changed from the first value to thesecond value.

In a second example, a measured rate of change for the flow rate for aprocess gas, such as a precursor-containing gas, into the thermalprocessing chamber, and the measured rate of change for the flow ratefor the process gas is determined as and/or after a gas system flowcontrol parameter (mass flow control valve position) is changed from afirst value to a second value.

In a third example, a measured rate of change for the chambertemperature can be determined, and the measured rate of change for thechamber temperature is determined as and/or after a temperature controlsystem parameter (heater power) is changed from a first power level to asecond power level.

In a fourth example, a measured rate of change for the chamber chemistrycan be determined, and the measured rate of change for the chamberchemistry is determined as and/or after a system parameter is changedfrom a first value to a second value.

In other examples, a measured rate of change for a deposited layer, anetched layer, a saturation state, or a contamination state can bedetermined.

Then, an inverse purging process model for the purging process can beexecuted that relates the first measured rate of change to a value for asecond parameter in the second set of the purging process parameters toobtain a predicted value for the second parameter.

In one example, an inverse model may relate a process gas flow rate, toa measured rate of change for chamber pressure. In a second example, aninverse model may relate a chamber chemistry state (a process by-productor contaminant concentration) in the thermal processing chamber to ameasured rate of change for chamber pressure. In a third example, aninverse model may relate a chamber chemistry state (a process by-productor contaminant concentration) in the thermal processing chamber to ameasured rate of change for a flow rate for a process gas. In a fourthexample, an inverse model may relate a wafer/substrate temperature to ameasured rate of change for chamber temperature and/or substrate holdertemperature. In other examples, an inverse model may relate a processand/or system parameter to a measured rate of change for a depositedlayer, an etched layer, a saturation state, or a contamination state.Alternatively, other rates of change and other process parameters may beused.

Finally, the dynamic estimation error for the purging process can becalculated using a difference between the predicted value for the secondparameter in the second set of the purging process parameters and anexpected value for the second parameter, and the expected value can bedetermined using a BIST rule for the purging process. The expected valuemay be a dynamically changing value, a measured value, a stored value, acalculated value, and/or a recipe setpoint. Alternatively, the dynamicestimation error may be calculated using a difference between apredicted value, a measured value, a calculated value, and/or historicalvalue for one or more process parameters.

In one example, the predicted value may be a predicted process gas flowrate and the expected value may be an expected process gas flow rate,and the process gas may include a precursor. In a second example, thepredicted value may be a predicted chamber chemistry state and theexpected value may be an expected chamber chemistry state. In otherexamples, the predicted and expected values may be depositionthicknesses, etching dimensions, saturation state values, orcontamination state values.

When creating process models for an MLD procedure being performed at lowpressures and using process recipes that include injecting a purging gasinto a thermal processing chamber that can include a plurality ofinjection/control zones, one or more models can be created that relate agas flow rate (GFR) for a process gas, such as a purging gas, to a rateof change for pressure (RCP) within the processing chamber and/or withinone or more injection/control zones in the processing chamber. Forexample, a rate of change can be expressed as a positive or negativenumber. Alternatively, a pressure rise rate (PRR) may be used.

For example, a simplified monitoring procedure for a purging processthat include creating a simplified model that relates a first processparameter, such as Purging Gas Flow Rate (PGFR), to the rate of changeof a second process parameter, such as a Rate of Change of Pressure(RCP). Then, for any given process recipe step while and/or after avalve opening is changed and a purging gas flow is introduced, aMeasured Rate of Change of Pressure (MRCP) can be obtained by monitoringthe real-time process parameters during the purging process. Next, usingthe MRCP and one or more models, a Predicted Purging Gas Flow Rate(PPGFR) can be calculated. Then, the PPGFR can be compared to anExpected Purging Gas Flow Rate (EPGFR)—the expected gas flow rate can beassociated with the purging gas and can be established by a setpoint inthe purging process recipe. A purging process dynamic estimation errorcan be calculated using the difference between the predicted value PPGFRand expected value EPGFR. The purging process dynamic estimation errorcan be compared to a limit established for the current operatingcondition. Alternatively, other process parameters and other rates ofchange may be used.

In 1245, a query can be performed to determine when to continue thepurging process. When the purging process is operating within limitsestablished for the purging process, procedure 1200 can branch to 1260.When the purging process is not operating within limits established forthe purging process, procedure 1200 can branch to 1250.

In one embodiment, the purging process dynamic estimation error iscompared to an operational limit established for one or more BIST rulesin the BIST table for the purging process. The purging process cancontinue when the purging process dynamic estimation error is within theoperational limit. When creating and or verifying BIST rules, a purgingprocess may be continued, paused, or stopped when the purging processdynamic estimation error is not within the operational limit. Forexample, operator and/or host intervention may be required.

In addition, the purging process dynamic estimation error can also becompared to a warning limit established for one or more BIST rules inthe BIST table for the purging process. The purging process can becontinued when the purging process dynamic estimation error is withinthe warning limit. The purging process can be paused and/or stopped whenthe purging process dynamic estimation error is not within the warninglimit.

When the purging process dynamic estimation error is not with theoperational limit, the purging process dynamic estimation error can thenbe compared to the warning limit; a warning message identifying apotential problem with the purging process and/or the MLD system can besent and the purging process can be continued when the purging processdynamic estimation error is within the warning limit.

When the purging process dynamic estimation error is not with thewarning limit, a fault message identifying a known problem with thepurging process and/or the MLD system can be sent and the purgingprocess can be stopped.

In various embodiments, warning messages can be sent that identifypotential problems with the purging process, the thermal processingchamber, the pressure control system coupled to the thermal processingchamber, the gas supply system coupled to the thermal processingchamber, the temperature control system coupled to the thermalprocessing chamber, the control system coupled to the thermal processingchamber, or a combination thereof.

In addition, fault messages can be sent that identify known problemswith the purging process, the thermal processing chamber, the pressurecontrol system coupled to the thermal processing chamber, the gas supplysystem coupled to the thermal processing chamber, the temperaturecontrol system coupled to the thermal processing chamber, the controlsystem coupled to the thermal processing chamber, or a combinationthereof.

For example, BIST rules may be used for chamber components, temperaturecontrol elements, pressure control components, gas system components,and/or controller components.

In addition, the rate of change for a purging process parameter and/orthe process drift value for the purging process can be monitored, andone or more notification messages can be sent when a purging processparameter and/or the process drift value for the purging process areapproaching an operational and/or warning limit.

In 1250, a query can be performed to determine when to modify themonitoring process for the purging process. When the purging processdynamic estimation error is not within the warning limit established forthe purging process, the controller can determine if a new purgingprocess model, a new BIST rule, or a new purging process recipe, or amaintenance procedure, or a combination thereof is required. During amonitoring procedure, a controller can be used to determine if thepurging process currently being performed is a new process or should beassociated with a new BIST rule. Procedure 1200 can branch to 1255 whena procedure modification can be made. Procedure 1200 can branch to 1260when a procedure modification cannot be made.

In 1255, the monitoring procedure can be modified. For example, a newBIST rule can be created for the purging process when a new BIST rule isrequired, the new BIST rule having new operational and warning limits,new tolerance values, and new messages and being based on at least onepre-existing BIST rule created for the process. The new BIST rule withthe new operational and warning limits and the new tolerance values canbe entered into a BIST table, and wafer processing can continue. A newprocess recipe can be established for the purging process when a newprocess recipe is required, the new process recipe can have new purgingprocess parameters and a new BIST rule associated therewith. The newpurging process parameters can have values within and/or outside ofnormal production limits. During normal production processing, the newpurging process parameters can have values within the normal productionlimits. During non-production processing, the new purging processparameters can have values outside the normal production limits. The newBIST rule and new process recipe can be entered into a BIST table whenthe new BIST rule is not in the BIST table, and wafer processing cancontinue using the new process recipe. In addition, a new purgingprocess model can be established.

The purging process can be paused or stopped when the monitoringprocedure cannot be modified or a maintenance procedure is required.

In 1260, a query can be performed to determine when another purgingprocess is required. When another purging process is required, procedure1200 can branch to 1240, and when another purging process is notrequired, procedure 1200 can branch to 1265. When the purging process isperformed multiple times and/or multiple purging processes areperformed, one or more different purging process models can be executedand one or more different purging process recipes can be used.

When a purging process is performed, a chamber venting process, achamber cleaning process, and/or an evacuation process can be performed.During the purging process, surface saturation/contamination zones canbe determined on the surface of at least one of the plurality of wafers,and a physical and/or virtual sensor may be used for determining one ormore parameters for one or more surface saturation/contamination zones.A purging gas can be introduced into the processing chamber during apurging process, and the purging gas can be used to substantiallyeliminate contaminants, such as the first process gas components,precursor molecules, and/or process by-products from the wafer surfacesand from the processing chamber. For example, this can cause theconcentration of reactant species (precursor) at each wafer surface(saturation zone) to be approximately zero. Alternatively, contaminationzones may be established for a wafer and/or processing chamber. Aprocess time for a purging process can be determined using limits in theBIST table.

The operational conditions for a purging process can include limits fora concentration level of un-reacted first precursor molecules; limitsfor a concentration level of a precursor gas; limits for a concentrationlevel of the purging gas; and limits for a concentration level ofby-products from the purging process. In one embodiment, the desiredvalue can be approximately zero. In alternate embodiments, the desiredvalue can be greater than zero.

In alternate embodiments, the operational conditions may require thatintelligent set points be used to control the uniformity of thedeposited layer on the wafers. Methods for computing the contaminationlevels at across-wafer locations and the sensitivity of thecontamination levels to purge gas flow set point variations have beendescribed above.

In one embodiment, when using a second precursor-containing gas that isused to react with a first precursor-containing gas, a surface reactionstate can be used, and a physical and/or virtual sensor can be used todetermine when the surface reaction state has reached a desired value.The surface reaction state can be used to determine when the secondprecursor has completely reacted with the monolayer of the firstprecursor material on the surfaces of the plurality of wafers, and asubstantially uniform film is deposited onto the surfaces of theplurality of wafers.

The operational conditions for a precursor process that uses a secondprecursor-containing gas can include: limits for the flow rate for thesecond precursor-containing gas; concentration values for one or moresecond reactant (R_(B)) species (precursor molecules); limits and modelsfor the flow between the wafers; limits for a residence time for thesecond reactant species (precursor molecules); models and limits fordetermining concentration value for the second reactant species for oneor more surface saturation zones; and models and limits for determininga reaction rate for one or more surface saturation zones. For example, adeposition process is dependent on saturated surface reactions between afirst precursor deposited on the surface of the wafers and a secondprecursor and may be a self-limiting reaction.

When a second purging process is performed, a second purging gas can beintroduced into the processing chamber during a purging process, and thesecond purging gas can be used to substantially eliminate contaminantscreated during a second precursor process, such as the secondprecursor-containing gas components, second precursor molecules, and/orprocess by-products from the wafer surfaces and from the processingchamber. For example, this can cause the concentration of the secondreactant species (precursor) at each wafer surface (saturation zone) tobe approximately zero. A process time for a second purging process canbe determined using limits in a BIST table.

The operational conditions for a second purging process can includelimits for a concentration level of un-reacted second precursormolecules; limits for a concentration level of a second precursor gas;limits for a concentration level of the second purging gas; and limitsfor a concentration level of by-products from the second purgingprocess. In one embodiment, the desired value can be approximately zero.In alternate embodiments, the desired value can be greater than zero.

In 1265, a query can be performed to determine when a different processis required. When an additional different process is required, procedure1200 can branch to 1270, and when an additional different process is notrequired, procedure 1200 can branch to 1275.

In 1270, one or more additional processes can be performed. When aprocess is stopped and/or paused, one or more wafers can be transferredto a storage location, and/or one or more wafers can be transferred to astorage location. In addition, after an error condition has beenanalyzed, one or more wafers can be transferred to a processing chamber.

In 1275, procedure 1200 can end. When procedure 1200 ends, one or morewafers can be removed from the processing chamber, transferred to astorage location, and/or transferred to a measurement tool.

For example, during procedure 1200, a second precursor can react with amonolayer of the first precursor material that has been adsorbed on thesurface of the plurality of wafers, thereby forming a monolayer ofdesired material, such as Si₃N₄, Al₂O₃, Ta₂O₅, and HfSiON on the surfaceof each of the plurality of wafers.

When process parameters include chamber pressure P_(c) the rate ofchange for chamber pressure during the process {dot over (P)}_(c) can bemodeled as:{dot over (P)}=ƒ ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)and a steady-state condition can be modeled as:P _(c)=ƒ_(g) ₁(p ₁ ,p ₂ , . . . , p _(n) ,v)

where p₁-p_(n) are each process parameters for the process other thanchamber pressure, v can be a process parameter related to a pressurecontrol element coupled to the thermal processing chamber, and P_(c) isthe chamber pressure measured in mTorr. For example, v can be a valveangle opening measured in percent. Alternatively, the opening can beexpressed as an angular position or an opening size. In addition, a pumpmay be used to control chamber pressure and it may be characterizedusing a pumping speed, a pumping volume, or a pressure difference.

When process parameters include chamber temperature T_(c), the rate ofchange for chamber temperature during the process {dot over (T)}_(c) canbe modeled as:{dot over (T)} _(c)=ƒ₂(p ₁ ,p ₂ , . . . , p _(n) ,h)and a steady-state condition can be modeled as:T _(c) =g ₂(p ₁ ,p ₂ , . . . , p _(n) ,h)where p₁-p_(n) are each process parameters for the process other thanchamber temperature, h can be a process parameter related to atemperature control element coupled to the thermal processing chamber.For example, h can be a heater power measured in watts. Alternatively,other heating and cooling devices may be used. In addition, the heatermay be characterized as a multi-zone device.

When process parameters include a reactant concentration R for areactant species and the rate of change for reactant concentrationduring the process {dot over (R)} can be modeled as:{dot over (R)}=ƒ ₃(p ₁ ,p ₂ , . . . , p _(n) ,r)and a steady-state condition can be modeled as:R=g ₃(p ₁ ,p ₂ , . . . , p _(n) ,r)where p₁-p_(n), are each process parameters for the process other thanreactant concentration, r can be a process parameter related to a gassystem control element coupled to the thermal processing chamber. Forexample, r can be a flow rate for a MFC measured in sccm. Alternatively,other gas system components may be used. In addition, a gas deliverysystem may be characterized as a multi-zone device. In alternateembodiments, the reactant concentration may include a chamber chemistrystate, or a contaminant state.

When process parameters include wafer temperature {dot over (T)}_(w),the rate of change for wafer temperature during the process {dot over(T)}_(w) can be modeled as:{dot over (T)} _(w)=ƒ₄(p ₁ ,p ₂ , . . . , p _(n) ,z)and a steady-state condition can be modeled as:T _(w) =g ₄(p ₁ ,p ₂ , . . . , p _(n) ,z)where p₁-p_(n), are each process parameters for the precursor processother than substrate temperature, z can be a process parameter relatedto a temperature control element coupled to the thermal processingchamber and/or substrate holder. For example, z can be a heater powermeasured in watts. Alternatively, other heating and cooling devices maybe used. In addition, the heaters may be characterized as multi-zonedevices.

The process model can be based on the type of wafer boat, the type,position, and quantity of wafers, the type of thermal processingchamber, and/or the recipe to be performed. For example, the pluralityof wafers can include curved and/or instrumented wafers, and the modelscan account for factors such as wafer curvature. When curved wafers arepositioned in the boat, the gap between two curved wafers is variable,and the heat transfer and gas flow can be variable.

FIG. 13 illustrates a simplified flow diagram of a method of creating aBIST table for the real-time monitoring of a processing system inaccordance with embodiments of the invention. Process 1300 can start in1310.

In various embodiments, BIST tables that include dynamic operationalconditions and dynamic models for real-time monitoring can be createdfor a MLD system, a thermal processing system, an etching system, adeposition system, a plating system, a polishing system, an implantsystem, a developing system, or a transfer system, or a combination oftwo or more thereof. In addition, BIST tables can be created for a MLDprocess, a thermal process, an etching process, a deposition process, aplating process, a polishing process, an implant process, a developingprocess, or a transfer process, or a combination of two or more thereof.

BIST tables can be established for subsystems including temperaturecontrol components, pressure control components, gas supply components,mechanical components, computing components, or software components, orcombinations thereof.

When creating a BIST table, a process can be performed in which one ormore of the processing parameters are changed from a first value to asecond value. For example, the first value and/or second value can bechosen to establish a normal, warning, or fault condition to occurduring a process. In other cases, the first value and/or second valuecan be chosen to magnify and/or amplify an error during a process.

An operational condition can be structured as follows:Error<=Operational Limit (OL) defines an Operational Condition;Error>(OL) and <=Warning Limit (WL) defines Warning Condition;Error>(WL) defines a Fault Condition.

Alternatively, other structures can be used.

A number of processes can be performed a number of times to establishoperational limits and warning limits that are expected to occur atdifferent times during one or more processes, and a set of BIST rulescan be created using the set of expected dynamic error conditions andtheir associated operational limits and warning limits.

One set of processes can be used to characterize system performance whenthe processing system is operating within the operational limits duringa process. In this case, the dynamic estimation errors are less than theoperational limits. For example, a number of processes can be performeda number of times to establish operational limits. These processes canbe performed with process parameters within operational limits. Theseprocesses can produce a set of errors expected during “normal”operation, and the set of expected errors can be used to establish theoperational limits. For example, operational limits can be made largeenough to allow for some process variation. Design of Experiments (DOE)techniques can be used to minimize the number of processes required togenerate operational limits.

Another set of processes can be used to characterize system performancewhen the processing system is operating just outside the operationallimits during a process. In these cases, the dynamic estimation errorscan be greater than the operational limits and less than the warninglimits. For example, a second set of processes can be performed a numberof times to establish warning limits. These processes can be performedwith one or more process parameters just outside the operational limits.These processes can produce a set of errors expected when the systemperformance is deviated slightly from “normal” operation, and the set oferrors can be used to establish the warning limits. For example, warninglimits can be made large enough to allow some process drift and/orcomponent degradation, and warning limits can be made small enough toensure that high quality wafers are produced. The warning limits canalso be used to predict and prevent failures from occurring. DOEtechniques can be used to minimize the number of processes required togenerate warning limits.

In 1320, BIST rules can be created for a first process. In oneembodiment, one or more precursor processes can be performed on thewafers positioned in the processing chamber in the processing system.The wafers can be positioned at different heights in the processingchamber, and the processing chamber can be sealed. The wafers caninclude production wafers, instrumented wafers, test wafers, or dummywafers, or combinations thereof. Alternatively, a plurality of wafers isnot required.

The processing system can obtain operational data and use theoperational data to establish one or more recipes to use during aprocess. In addition, the operational data can include dynamic and/orstatic modeling information for predicting the performance of theprocessing system during the process. Furthermore, the data can includemeasured and/or predicted data from previous runs. Operationalconditions can also be used to establish a pre-processing state. Forexample, chamber pressure, chamber temperature, wafer temperature,and/or process gas conditions can be changed to operational values.

When creating BIST rules, one or more process models can be createdusing a set of nonlinear differential equations {dot over (x)}₁ and anoutput equation y₁, where{dot over (x)} ₁=ƒ(x ₁ ,p ₁ ,u ₁)+w ₁y ₁ =g(x ₁ ,p ₁ ,u ₁)+v ₁and the vector x₁ comprises a state vector for the process, the vectorp₁ comprises one or more modeling parameters for the process, the vectoru₁ comprises one or more inputs applied to the process, w₁ is a firstadditive white noise value having a zero mean, and v₁ is a secondadditive white noise value having a zero mean.

In one embodiment, the creation procedure can include measuring a rateof change for at least one parameter of a first set of processparameters as a first parameter in a second set of process parameters ischanged from a first value to a second value. The second set of processparameters does not include the at least one parameter of the first setof process parameters. The measured rate of change can be determined bymonitoring one or more process parameters in real-time as and/or afterthe first parameter of the second set is changed from a first value to asecond value. For example, the monitoring process may include measuringa rate of change for chamber pressure as and/or after a valve and/orpump parameter is changed from a first value to a second value.

One process model can relate a rate of change for the at least oneparameter of the first set to the second set of process parameters asand/or after the first parameter in the second set is changed from afirst value to a second value. The second set of process parameters doesnot include the at least one parameter of the first set.

In some processing systems, an exhaust system can be coupled to theprocessing chamber, and the exhaust system can include a gate valve andthe chamber pressure change rate can be dependent on the gate valveopening. For example, the BIST rules, the operational conditions, and/orprocess models may relate a rate of change for chamber pressure to thesecond set of process parameters that does not include chamber pressureas and/or after a valve opening is changed from a first position to asecond position.

In addition, another model (inverse model) can be used with the measuredrate of change to obtain a predicted value for a second parameter in thesecond set of process parameters. For example, another model (inversemodel) may relate the second parameter, which may be a gas flow rate, tothe measured rate of change for chamber pressure. Alternatively, otherrates of change and other process parameters may be used.

The predicted value for the process parameter can be compared to anexpected value for the process parameter. The expected value may be adynamically changing value, a measured value, a stored value, acalculated value, and/or a recipe setpoint. For example, the predictedvalue may be a predicted gas flow rate and the expected value may be anexpected gas flow rate.

During the creation, one or more dynamic estimation errors can becalculated using the differences between the predicted values for theprocess parameters and the expected values for the process parameters.For example, dynamic estimation errors may be calculated using thedifference between a predicted gas flow rate and an expected gas flowrate. The table can include data for single gas flow rates and multi-gasflow rates. Alternatively, the dynamic estimation error may becalculated using a difference between a predicted value, a measuredvalue, a calculated value, and/or historical value for a processparameter. BIST rules can be created for monitoring processes usingrates of change for chamber pressure.

In some processing systems, a temperature control system can be coupledto the processing chamber, and the temperature control system caninclude a heater and the chamber temperature change rate can bedependent on the heater power. For example, a process model may relate arate of change for chamber temperature to the second set of processparameters that does not include chamber temperature as and/or after aheater power is changed from a first power level to a second powerlevel. In addition, another model (inverse model) may relate a reactionrate to the measured rate of change for chamber temperature, and adynamic estimation error may be calculated using the difference betweenthe predicted value for a reaction rate and the expected value for thereaction rate. BIST rules can be created for monitoring processes usingrates of change for chamber temperature.

In some processing systems, a temperature control system can be coupledto a wafer holder in a processing chamber, and the temperature controlsystem can include a wafer heater in the wafer holder and the wafertemperature change rate can be dependent on the heater power provided towafer heater. For example, a process model may relate a rate of changefor wafer temperature to the second set of process parameters that doesnot include wafer temperature as and/or after the wafer heater power ischanged from a first power level to a second power level. In addition,another model (inverse model) may relate a flow rate for a backside gasto the measured rate of change for wafer temperature, and a dynamicestimation error may be calculated using the difference between thepredicted value for a flow rate for a backside gas and the expectedvalue for flow rate for a backside gas. BIST rules can be created formonitoring processes using rates of change for wafer temperature.

In one embodiment, the creation process can include measuring a rate ofchange for at least one parameter of a first set of process parametersas at least one parameter of a second set of process parameters ischanged. The measured rate of change can be determined by monitoring oneor more process parameters in real-time during the first process.Alternatively, the creation process may include measuring a rate ofchange for at least one parameter of a first set of process parametersafter at least one parameter of a second set of process parameters ischanged. In addition, the creation process can include measuring a rateof change for at least one parameter of a first set of processparameters as at least one parameter of a second set of processparameters is maintained at a substantially constant value.

For example, a new BIST rule may be created for a process when a dynamicestimation error calculated for the process cannot be associated with aBIST rule in the BIST table, and a creation procedure may be pausedand/or stopped when a new BIST rule cannot be created.

In addition, new operational limits can be established for the new BISTrule. In one embodiment, the new operational limits for the new BISTrule are based on the operational limits associated with the dynamicestimation error for the process. Alternatively, new operational limitsmay be determined independently.

In one embodiment, new warning limits can be established based on thenew operational limits. Alternatively, new warning limits may bedetermined independently.

A warning message can be created and associated with the new BIST rule.For example, this warning message can be sent when the dynamicestimation error is outside the operational limits but within the newwarning limits established for the new BIST rule. A fault message canalso be created and associated with the new BIST rule. For example, thisfault message can be sent when the dynamic estimation error is notwithin the new warning limits established for the new BIST rule. Duringa creation procedure, process parameters may be changed to values thatcause fault conditions so that a more complete BIST table is created.

In other cases, new real-time dynamic models can be created and/orexecuted to generate new BIST rules. For example, new process models canbe created for new rates of change and/or new predicted parametervalues. In addition, new expected values may be used and new dynamicestimation errors can be calculated. In addition, new dynamic estimationerrors may be calculated using different predicted, measured,calculated, and/or historical values for the process parameters.

Procedure 1300 can end in 1330.

BIST rules can be created and used during pre-processing. For example,the pressure in a processing chamber may be dynamically changed from afirst pressure to an operating pressure, and a BIST rule can be used tomonitor chamber pressure error and a warning or fault message can besent when the chamber is not sealed properly. In addition, theprocessing chamber temperature can be changed from a first temperatureto an operational temperature during a pre-processing time, and a BISTrule can be used to monitor chamber temperature error and a warning orfault message can be sent when the heater has failed. Furthermore, thechamber chemistry can be changed during a pre-processing time, and aBIST rule may be used to monitor chamber chemistry error and a warningor fault message can be sent when a gas supply system component hasfailed.

The process dynamic estimation error can be used to establish new BISTrules and/or new operational conditions and/or confirm current data.

Physical and/or virtual sensors can be used to create and/or verify BISTrules, models, operational conditions, and measured values. For example,a measured rate of change for the processing chamber can includemeasuring temperature for each of the plurality of temperature controlzones. Alternatively, measurements may not be required for each zone. Inother embodiments, optical techniques can be used to measure temperaturein the chamber and/or the wafer temperature.

One or more measured dynamic process responses can be created during aprocess. The measured dynamic process response can be created each timeone or more of the processing parameters is changed from a first valueto a second value during a process. When a process is performed multipletimes, one or more different measured dynamic process responses can becreated. Process-related differences between measured dynamic processresponses can be calculated when new measured dynamic process responsesare created.

Alternatively, a dynamic estimation error can be determined using adifference between a predicted dynamic process response and a measureddynamic process response each time one or more of the processingparameters is changed during a process. Furthermore, the dynamicestimation error can be compared to operational thresholds establishedby one or more rules in a BIST table each time a new dynamic estimationerror is determined during a process. The process can continue when thedynamic estimation error is within the operational thresholdsestablished by one or more rules in the BIST table. In this case, theprocessing system is operating within the operational limits during theprocess. Techniques for creating and using BIST tables are taught inco-pending U.S. patent application Ser. Nos. 11/217,230 and 11/217,276(Attorney Docket Nos. TPS-006 and TPS-021), each entitled “BUILT-IN SELFTEST FOR A THERMAL PROCESSING SYSTEM” and each filed on Sep. 1, 2005,and both of which are incorporated by reference herein in theirentirety.

In an alternate embodiment, when a process parameter is changed from afirst set point value to a second set point value, the change can occurin a series of steps. A BIST rule, an operational condition, and/or areal-time dynamic model may be created/executed/verified for each step.

The operational conditions data can include predicted dynamic processresponses, predicted dynamic thermal profiles, predicted dynamic chamberpressures, predicted dynamic gas flows, predicted chamber chemistries,predicted flow profiles, or predicted process times, or a combinationthereof.

When a deposition procedure is performed, a uniform thickness can bedeposited in each deposition cycle. Since the film is grown in alayer-by-layer mode, and the total film thickness is determined by thenumber of deposition cycles, the use of low-pressure process models inthe invention increases the throughput by processing a number of wafersat one time and reducing the time required for each deposition cycle.The invention can provide for faster rates of change for processparameters that can lead to increased throughput, and can provideimproved uniformity and step coverage on wafers having high aspect ratiofeatures. Furthermore, using the modeling techniques of the presentinvention in etching processes can provide improved uniformity withinhigh aspect ratio features including improved critical dimension (CD)control and profile uniformity control.

While the present invention has been illustrated by a description ofvarious embodiments and while these embodiments have been described inconsiderable detail, it is not the intention of the applicants torestrict or in any way limit the scope of the appended claims to suchdetail. Additional advantages and modifications will readily appear tothose skilled in the art. The invention in its broader aspects istherefore not limited to the specific details, representative apparatusand methods, and illustrative examples shown and described. Accordingly,departures may be made from such details without departing from thescope of applicants' general inventive concept.

1. A method of monitoring a processing system in real-time, comprising:performing a first process on one or more wafers positioned within aprocessing chamber having a reduced pressure; monitoring the firstprocess using a first set of nonlinear differential equations {dot over(x)}₁ and a first output equation y₁, wherein{dot over (x)} ₁=ƒ(x ₁ ,p ₁ ,u ₁)+w ₁y ₁ =g(x ₁ ,p ₁ ,u ₁)+v ₁  and x₁, p₁, and u₁ are first processparameters in which the first vector x₁ comprises a first state vector,the first vector p₁ comprises one or more modeling parameters for thefirst process, the vector u₁ comprises one or more inputs applied to thefirst process, w₁ is a first additive white noise value having a zeromean, and v₁ is a second additive white noise value having a zero mean;determining a first process model for the first process that relates afirst rate of change for at least one parameter of a first set of thefirst process parameters to a second set of the first process parametersas and/or after a first parameter in the second set is changed from afirst value to a second value, wherein the second set does not includethe at least one parameter of the first set; determining a firstmeasured rate of change for the at least one parameter of the first setin real time as and/or after the first parameter in the second set ischanged from the first value to the second value; executing a firstinverse process model for the first process that relates the firstmeasured rate of change to a value for a second parameter in the secondset of first process parameters to obtain a predicted value for thesecond parameter in the second set; calculating a first dynamicestimation error for the first process; comparing the first dynamicestimation error to a first operational limit established for the firstprocess; continuing the first process when the first dynamic estimationerror is within the first operational limit; and examining the firstprocess when the first dynamic estimation error is not within the firstoperational limit.
 2. The method of claim 1, wherein the first dynamicestimation error is calculated using a difference between the predictedvalue for the second parameter and an expected value for the secondparameter, wherein the expected value for the second parameter isdetermined using a process recipe, an operational condition and/or BISTrule for the first process.
 3. The method of claim 1, wherein the firstoperational limit is established by a threshold determined for one ormore BIST rules in a BIST table for the first process.
 4. The method ofclaim 1, further comprising: comparing the first dynamic estimationerror to a first warning limit established for the first process;sending a warning message and continuing the first process when thefirst dynamic estimation error is within the first warning limit; andsending a fault message and determining if a new process model, a newBIST rule, a new process recipe, or a maintenance procedure, or acombination thereof, is required when the first dynamic estimation erroris not within the first warning limit.
 5. The method of claim 4, furthercomprising: determining a new first process model for the first processwhen a new process model is required, wherein the new first processmodel relates a new first rate of change for at least one new parameterof a new first set of first process parameters to a new second set offirst process parameters as and/or after a new first parameter in thenew second set is changed from a new first value to a new second value,wherein the new second set of first process parameters does not includethe at least one new parameter of the new first set; and processing anadditional wafer using the new first process model.
 6. The method ofclaim 4, further comprising: creating a new BIST rule for the firstprocess when a new BIST rule is required, the new BIST rule having newoperational and warning limits, new tolerance values, and new messagesand being based on at least one pre-existing BIST rule created for thefirst process; entering the new BIST rule with the new operationallimits and the new tolerance values into a BIST table; and continuing toprocess wafers.
 7. The method of claim 4, further comprising:establishing a new process recipe for the first process when a newprocess recipe is required, the new process recipe having new processparameters and a new BIST rule associated therewith; entering the newBIST rule and new process recipe into a BIST table for the first processwhen the new BIST rule is not in the BIST table; and continuing toprocess wafers using the new process recipe.
 8. The method of claim 4,further comprising: stopping the first process when a new BIST rulecannot be created, or a new process recipe cannot be established, or amaintenance procedure is required.
 9. The method of claim 1, wherein theprocessing system comprises a thermal processing system, an etchingsystem, a deposition system, a plating system, a polishing system, animplant system, a developing system, or a transfer system, or acombination of two or more thereof.
 10. The method of claim 1, whereinthe first process comprises a thermal process, an etching process, adeposition process, a plating process, a polishing process, an implantprocess, a developing process, or a transfer process, or a combinationof two or more thereof.
 11. The method of claim 1, wherein the at leastone parameter of the first set includes chamber pressure and a chamberpressure change rate {dot over (P)}_(c) is modeled as:{dot over (P)} _(c)=ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) and a steady-statecondition is modeled as:P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) where p₁-p_(n) are each firstprocess parameters other than chamber pressure, v is a first processparameter related to a valve coupled to the processing chamber, and p isthe chamber pressure measured in mTorr.
 12. The method of claim 1,wherein the at least one parameter of the first set includes chamberpressure and a chamber pressure change rate {dot over (P)}_(c) ismodeled as:{dot over (P)} _(c)=ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) and a steady-statecondition is modeled as:P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) where p₁-p_(n), are each firstprocess parameters other than chamber pressure, v is a first processparameter related to a pump coupled to the processing chamber, and p isthe chamber pressure measured in mTorr.
 13. The method of claim 1,wherein the at least one parameter of the first set includes chambertemperature and a chamber temperature change rate {dot over (T)}_(c) ismodeled as:{dot over (T)} _(c)=ƒ₂(p ₁ ,p ₂ , . . . , p _(n) ,h) and a steady-statecondition is modeled as:T _(c) =g ₂(p ₁ ,p ₂ , . . . , p _(n) ,h) where p₁-p_(n) are each firstprocess parameters other than chamber temperature, h is a first processparameter related to a temperature control element coupled to theprocessing chamber, and T_(c) is the chamber temperature measured indegrees Celsius.
 14. The method of claim 1, wherein the at least oneparameter of the first set includes a reactant concentration for areactant species and a reactant concentration change rate {dot over (R)}is modeled as:{dot over (R)}=ƒ ₃(p ₁ ,p ₂ , . . . , p _(n) ,r) and a steady-statecondition is modeled as:R=g ₃(p ₁ ,p ₂ , . . . , p _(n) ,r) where p₁-p_(n) are each firstprocess parameters other than reactant concentration, r is a firstprocess parameter related to a flow control element coupled to theprocessing chamber, and R represents a reactant concentration inpercent.
 15. The method of claim 1, wherein the at least one parameterof the first set parameters includes wafer temperature and a wafertemperature change rate {dot over (T)}_(w) is modeled as:{dot over (T)} _(w)=ƒ₄(p ₁ ,p ₂ , . . . , p _(n) ,z) and a steady-statecondition is modeled as:T _(w) =g ₄(p ₁ ,p ₂ , . . . , p _(n) ,z) where p₁-p_(n) are each firstprocess parameters other than wafer temperature, z is a first processparameter related to a temperature control element coupled to asubstrate holder in the processing chamber, and T_(w) is the wafertemperature measured in degrees Celsius.
 16. The method of claim 1,further comprising: changing the first parameter in the second set offirst process parameters using a series of steps; determining the firstprocess model using the series of steps; determining the measured firstrate of change using the series of steps; executing the first inverseprocess model using the series of steps; and calculating the firstdynamic estimation error using the series of steps.
 17. The method ofclaim 1, further comprising: establishing a plurality of measurementzones in the one or more wafers in the processing chamber; determiningthe first process model using the plurality of measurement zones;determining the measured first rate of change using the plurality ofmeasurement zones; executing the first inverse process model using theplurality of measurement zones; and calculating the first dynamicestimation error using the plurality of measurement zones.
 18. Themethod of claim 1, further comprising: establishing a plurality of zonesin the processing chamber; determining the first process model using theplurality of zones in the processing chamber; determining the measuredfirst rate of change using the plurality of zones in the processingchamber; executing the first inverse process model using the pluralityof zones in the processing chamber; and calculating the first dynamicestimation error using the plurality of zones in the processing chamber.19. The method of claim 1, further comprising: establishing a pluralityof temperature control zones in the processing chamber; modeling athermal interaction between the temperature control zones of theprocessing chamber; and incorporating the model of the thermalinteraction into the first process model, or the first inverse processmodel, or a combination thereof.
 20. The method of claim 1, furthercomprising: establishing a plurality of gas flow control zones in theprocessing chamber; modeling a flow interaction between the gas flowcontrol zones of the processing chamber; and incorporating the model ofthe flow interaction into the first process model, or the first inverseprocess model, or a combination thereof.
 21. The method of claim 1,further comprising: modeling a thermal interaction between the one ormore wafers and a processing space within the processing chamber; andincorporating the model for the thermal interaction into the firstprocess model, or the first inverse process model, or a combinationthereof.
 22. The method of claim 1, further comprising: creating a wafercurvature model when the one or more wafers includes one or more curvedwafers; and incorporating the wafer curvature model into the firstprocess model, or the first inverse process model, or a combinationthereof.
 23. The method of claim 1, the performing a process furthercomprising: determining values for the vector x₁, the vector p₁, thevector u₁, and the noise terms w₁ and v₁ using a first set of processrecipes, a first set of component characteristics, a first set ofassumptions, a first set of operational conditions, or a first set ofBIST rules, or a combination thereof.
 24. The method of claim 1, furthercomprising: obtaining historical data; and using the historical data todetermine the first process, the first process model, or the firstinverse process model, or a combination thereof.
 25. The method of claim1, wherein a difference between the first dynamic estimation error forthe first process and the first operational limit established for thefirst process is monitored to predict potential problems.
 26. The methodof claim 4, wherein a difference between the first dynamic estimationerror for the first process and the first warning limit established forthe first process is monitored to predict potential problems.
 27. Themethod of claim 1, further comprising: performing a second process onthe one or more wafers positioned within the processing chamber havingthe reduced pressure; monitoring the second process using a second setof nonlinear differential equations {dot over (x)}₂ and a second outputequation y₂, wherein{dot over (x)} ₂=ƒ(x ₂ ,p ₂ ,u ₂)+w ₂y ₂ =g(x ₂ ,p ₂ ,u ₂)+v ₂ and x₂, p₂, and u₂ are second processparameters in which the second vector x₂ comprises a second statevector, the second vector p₂ comprises one or more modeling parametersfor the second process, the second vector u₂ comprises one or moreinputs applied to the second process, w₂ is a third additive white noisevalue having a zero mean, and v₂ is a fourth additive white noise valuehaving a zero mean; determining a second process model for the secondprocess that relates a second rate of change for at least one parameterof a third set of the second process parameters to a fourth set of thesecond process parameters as and/or after a third parameter in thefourth set is changed from a third value to a fourth value, wherein thefourth set does not include the at least one parameter of the third set;determining a second measured rate of change for the at least oneparameter of the third set, wherein the second measured rate of changeis determined in real time as and/or after the third parameter ischanged from the third value to the fourth value; executing a secondinverse process model for the second process that relates the secondmeasured rate of change to a value for a fourth parameter in the fourthset of second process parameters to obtain a predicted value for thefourth parameter; calculating a second dynamic estimation error for thesecond process; comparing the second dynamic estimation error for thesecond process to a second operational limit established for the secondprocess; continuing the second process when the second dynamicestimation error is within the second operational limit; and examiningthe second process when the second dynamic estimation error is notwithin the second operational limit.
 28. The method of claim 27, whereinthe second dynamic estimation error is calculated using a differencebetween the predicted value for the fourth parameter and an expectedvalue for the fourth parameter, wherein the expected value for thefourth parameter is determined using a process recipe, an operationalcondition and/or BIST rule for the second process.
 29. The method ofclaim 27, wherein the second operational limit is established by athreshold determined for one or more BIST rules in a BIST table for thesecond process.
 30. The method of claim 27, further comprising:comparing the second dynamic estimation error for the second process toa second warning limit established for the second process; sending awarning message and continuing the second process when the seconddynamic estimation error is within the second warning limit; and sendinga fault message and determining if a new process model, a new BIST rule,or a new process recipe, or a maintenance procedure, or a combinationthereof is required when the second dynamic estimation error is notwithin the second warning limit.
 31. The method of claim 30, furthercomprising: determining a new second process model for the secondprocess when a new process model is required, wherein the new secondprocess model relates a new second rate of change for at least one newparameter of a new third set of second process parameters to a newfourth set of second process parameters as and/or after a new thirdparameter in the new fourth set is changed from a new third value to anew fourth value, wherein the new fourth set does not include the atleast one new parameter of the new third set; and processing one or moreadditional wafers using the new second process model.
 32. The method ofclaim 30, further comprising: creating a new BIST rule for the secondprocess when a new BIST rule is required, the new BIST rule having newoperation and warning limits, new tolerance values, and new messages andbeing based on at least one pre-existing BIST rule created for thesecond process; entering the new BIST rule with the new operationallimits and the new tolerance values into a BIST table; and continuing toprocess wafers.
 33. The method of claim 30, further comprising:establishing a new process recipe for the second process when a newprocess recipe is required, the new process recipe having new processparameters and a new BIST rule associated therewith; entering the newBIST rule and new process recipe into a BIST table when the new BISTrule is not in the BIST table; and processing an additional wafer usingthe new process recipe.
 34. The method of claim 30, further comprising:stopping the second process when a new BIST rule cannot be created, or anew process recipe cannot be established, or a maintenance procedure isrequired.
 35. The method of claim 27, wherein the processing systemcomprises a thermal processing system, an etching system, a depositionsystem, a plating system, a polishing system, an implant system, adeveloping system, or a transfer system, or a combination of two or morethereof.
 36. The method of claim 27, wherein the second processcomprises a thermal process, an etching process, a deposition process, aplating process, a polishing process, an implant process, a developingprocess, or a transfer process, or a combination of two or more thereof.37. The method of claim 27, wherein the at least one parameter of thethird set includes chamber pressure and a chamber pressure change rate{dot over (P)}_(c) is modeled as:{dot over (P)} _(c)=ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) and a steady-statecondition is modeled as:P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) where p₁-p_(n) are each secondprocess parameters other than chamber pressure, v is a second processparameter related to a valve coupled to the processing chamber, and p isthe chamber pressure measured in mTorr.
 38. The method of claim 27,wherein the at least one parameter of the third set includes chamberpressure and a chamber pressure change rate {dot over (P)}_(c) ismodeled as:{dot over (P)} _(c)=ƒ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) and a steady-statecondition is modeled as:P _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,v) where p₁-p_(n) are each secondprocess parameters other than chamber pressure, v is a second processparameter related to a pump coupled to the processing chamber, and p isthe chamber pressure measured in mTorr.
 39. The method of claim 27,wherein the at least one parameter of the third set includes chambertemperature and a chamber temperature change rate {dot over (T)}_(c) ismodeled as:{dot over (T)} _(c)=ƒ₂(p ₁ ,p ₂ , . . . , p _(n) ,h) and a steady-statecondition is modeled as:T _(c) =g ₁(p ₁ ,p ₂ , . . . , p _(n) ,h) where p₁-p_(n) are each secondprocess parameters other than chamber temperature, h is a second processparameter related to a temperature control element coupled to theprocessing chamber, and T is the chamber temperature measured in degreesCelsius.
 40. The method of claim 27, wherein the at least one parameterof the third set includes a reactant concentration for a reactantspecies and a reactant concentration change rate {dot over (R)} ismodeled as:{dot over (R)}=ƒ ₃(p ₁ ,p ₂ , . . . , p _(n) ,r) and a steady-statecondition is modeled as:R=g ₃(p ₁ ,p ₂ , . . . , p _(n) ,r) where p₁-p_(n) are each secondprocess parameters other than reactant concentration, r is a secondprocess parameter related to a flow control element coupled to theprocessing chamber, and R represents a reactant concentration inpercent.
 41. The method of claim 27, wherein the at least one parameterof the third set includes wafer temperature and a wafer temperaturechange rate {dot over (T)} _(w) is modeled as:{dot over (T)} _(w)=ƒ₄(p ₁ ,p ₂ , . . . , p _(n) ,z) and a steady-statecondition is modeled as:T _(w) =g ₄(p ₁ ,p ₂ , . . . , p _(n) ,z) where p₁-p_(n) are each secondprocess parameters other than wafer temperature, z is a second processparameter related to a temperature control element coupled to asubstrate holder in the processing chamber, and T_(w) is the wafertemperature measured in degrees Celsius.
 42. The method of claim 27,further comprising: changing the third parameter in the fourth set usinga series of steps; determining the second process model using the seriesof steps; determining the measured second rate of change using theseries of steps; executing the second inverse process model using theseries of steps; and calculating the second dynamic estimation errorusing the series of steps.
 43. The method of claim 27, furthercomprising: establishing a plurality of measurement zones in the one ormore wafers in the processing chamber; determining the second processmodel using the plurality of measurement zones; determining the measuredsecond rate of change using the plurality of measurement zones;executing the second inverse process model using the plurality ofmeasurement zones; and calculating the second dynamic estimation errorusing the plurality of measurement zones.
 44. The method of claim 27,further comprising: establishing a plurality of zones in the processingchamber; determining the second process model using the plurality ofzones in the processing chamber; determining the measured second rate ofchange using the plurality of zones in the processing chamber; executingthe second inverse process model using the plurality of zones in theprocessing chamber; and calculating the second dynamic estimation errorusing the plurality of zones in the processing chamber.
 45. The methodof claim 27, further comprising: establishing a plurality of temperaturecontrol zones in the processing chamber; modeling a thermal interactionbetween the temperature control zones of the processing chamber; andincorporating the model of the thermal interaction into the secondprocess model, or the second inverse process model, or a combinationthereof.
 46. The method of claim 27, further comprising: establishing aplurality of gas flow control zones in the processing chamber; modelinga flow interaction between the gas flow control zones of the processingchamber; and incorporating the model of the flow interaction into thesecond process model, or the second inverse process model, or acombination thereof.
 47. The method of claim 27, further comprising:modeling a thermal interaction between the one or more wafers and aprocessing space within the processing chamber; and incorporating themodel for the thermal interaction into the second process model, or thesecond inverse process model, or a combination thereof.
 48. The methodof claim 27, further comprising: creating a wafer curvature model whenthe one or more wafers includes one or more curved wafers; andincorporating the wafer curvature model into the second process model,or the second inverse process model, or a combination thereof.
 49. Themethod of claim 27, the performing a process further comprising:determining values for the vector x₂, the vector p₂, the vector u₂, andthe noise terms w₂ and v₂ using a second set of process recipes, asecond set of component characteristics, a second set of assumptions, asecond set of operational conditions, or a second set of BIST rules, ora combination thereof.
 50. The method of claim 27, further comprising:obtaining historical data; and using the historical data to determinethe second process, the second process model, or the second inverseprocess model, or a combination thereof.
 51. The method of claim 27,further comprising: obtaining wafer state data; and using the waferstate data to determine the second process, the second process model, orthe second inverse process model, or a combination thereof.
 52. Acomputer-readable medium comprising computer-executable instructionsfor: performing a first process on one or more wafers positioned withina processing chamber having a reduced pressure; monitoring the firstprocess using a first set of nonlinear differential equations {dot over(x)}₁ and a first output equation y₁, wherein{dot over (x)} ₁=ƒ(x ₁ ,p ₁ , . . . ,u ₁)+w ₁y ₁ =g(x ₁ ,p ₁ , . . . ,u ₁)+v ₁ and x₁, p₁, and u₁ are first processparameters in which the first vector x₁ comprises a first state vector,the first vector _(p) comprises one or more modeling parameters for thefirst process, the vector u₁ comprises one or more inputs applied to thefirst process, w₁ is a first additive white noise value having a zeromean, and v₁ is a second additive white noise value having a zero mean;determining a first process model for the first process that relates afirst rate of change for at least one parameter of a first set of thefirst process parameters to a second set of the first process parametersas and/or after a first parameter in the second set is changed from afirst value to a second value, wherein the second set does not includethe at least one parameter of the first set; determining a firstmeasured rate of change for the at least one parameter of the first setin real time as and/or after the first parameter in the second set ischanged from the first value to the second value; executing a firstinverse process model for the first process that relates the firstmeasured rate of change to a value for a second parameter in the secondset of first process parameters to obtain a predicted value for thesecond parameter in the second set; calculating a first dynamicestimation error for the first process; comparing the first dynamicestimation error to a first operational limit established for the firstprocess; continuing the first process when the first dynamic estimationerror is within the first operational limit; and examining the firstprocess when the first dynamic estimation error is not within the firstoperational limit.
 53. The computer-readable medium as claimed in claim52, further comprising computer-executable instructions for: performinga second process on the one or more wafers positioned within theprocessing chamber having the reduced pressure; monitoring the secondprocess using a second set of nonlinear differential equations {dot over(x)}₂ and a second output equation y₂, wherein{dot over (x)} ₂=ƒ(x ₂ ,p ₂ , . . . ,u ₂)+w ₂y ₂=g(x ₂ ,p ₂ , . . . ,u ₂)+v ₂ and x₂, p₂, and u₂ are second processparameters in which the second vector x₂ comprises a second statevector, the second vector p₂ comprises one or more modeling parametersfor the second process, the second vector u₂ comprises one or moreinputs applied to the second process, w₂ is a third additive white noisevalue having a zero mean, and v₂ is a fourth additive white noise valuehaving a zero mean; determining a second process model for the secondprocess that relates a second rate of change for at least one parameterof a third set of the second process parameters to a fourth set of thesecond process parameters as and/or after a third parameter in thefourth set is changed from a third value to a fourth value, wherein thefourth set does not include the at least one parameter of the third set;determining a second measured rate of change for the at least oneparameter of the third set, wherein the second measured rate of changeis determined in real time as and/or after the third parameter ischanged from the third value to the fourth value; executing a secondinverse process model for the second process that relates the secondmeasured rate of change to a value for a fourth parameter in the fourthset of second process parameters to obtain a predicted value for thefourth parameter; calculating a second dynamic estimation error for thesecond process; comparing the second dynamic estimation error for thesecond process to a second operational limit established for the secondprocess; continuing the second process when the second dynamicestimation error is within the second operational limit; and examiningthe second process when the second dynamic estimation error is notwithin the second operational limit.
 54. A method of operating acontroller in a processing system configured to process a substrate, themethod comprising the steps of: instructing the processing system toperform a first process on one or more wafers positioned within aprocessing chamber having a reduced pressure; instructing the processingsystem to monitor the first process using a first set of nonlineardifferential equations {dot over (x)}₁ and a first output equation y₁,wherein{dot over (x)} ₁=ƒ(x ₁ ,p ₁ , u ₁)+w ₁y ₁ =g(x ₁ ,p ₁ , u ₁)+v ₁ and x₁, p₁, and u₁ are first processparameters in which the first vector x₁ comprises a first state vector,the first vector p₁ comprises one or more modeling parameters for thefirst process, the vector u₁ comprises one or more inputs applied to thefirst process, w₁ is a first additive white noise value having a zeromean, and v₁ is a second additive white noise value having a zero mean;instructing the processing system to determine a first process model forthe first process that relates a first rate of change for at least oneparameter of a first set of the first process parameters to a second setof the first process parameters as and/or after a first parameter in thesecond set is changed from a first value to a second value, wherein thesecond set does not include the at least one parameter of the first set;instructing the processing system to determine a first measured rate ofchange for the at least one parameter of the first set in real time asand/or after the first parameter in the second set is changed from thefirst value to the second value; instructing the processing system toexecute a first inverse process model for the first process that relatesthe first measured rate of change to a value for a second parameter inthe second set of first process parameters to obtain a predicted valuefor the second parameter in the second set; instructing the processingsystem to calculate a first dynamic estimation error for the firstprocess; instructing the processing system to compare the first dynamicestimation error to a first operational limit established for the firstprocess; instructing the processing system to continue the first processwhen the first dynamic estimation error is within the first operationallimit; and instructing the processing system to examine the firstprocess when the first dynamic estimation error is not within the firstoperational limit.
 55. The method of operating a controller as claimedin claim 54, further comprising steps for: instructing the processingsystem to perform a second process on the one or more wafers positionedwithin the processing chamber having the reduced pressure; instructingthe processing system to monitor the second process using a second setof nonlinear differential equations {dot over (x)}₂ and a second outputequation y₂, wherein{dot over (x)} ₂=ƒ(x ₂ ,p ₂ , u ₂)+w ₂y ₂ =g(x ₂ ,p ₂ , u ₂)+v ₂ and x₂, p₂, and u₂ are second processparameters in which the second vector x₂ comprises a second statevector, the second vector p₂ comprises one or more modeling parametersfor the second process, the second vector u₂ comprises one or moreinputs applied to the second process, w₂ is a third additive white noisevalue having a zero mean, and v₂ is a fourth additive white noise valuehaving a zero mean; instructing the processing system to determine asecond process model for the second process that relates a second rateof change for at least one parameter of a third set of the secondprocess parameters to a fourth set of the second process parameters asand/or after a third parameter in the fourth set is changed from a thirdvalue to a fourth value, wherein the fourth set does not include the atleast one parameter of the third set; instructing the processing systemto determine a second measured rate of change for the at least oneparameter of the third set, wherein the second measured rate of changeis determined in real time as and/or after the third parameter ischanged from the third value to the fourth value; instructing theprocessing system to execute a second inverse process model for thesecond process that relates the second measured rate of change to avalue for a fourth parameter in the fourth set of second processparameters to obtain a predicted value for the fourth parameter;instructing the processing system to calculate a second dynamicestimation error for the second process; instructing the processingsystem to compare the second dynamic estimation error for the secondprocess to a second operational limit established for the secondprocess; instructing the processing system to continue the secondprocess when the second dynamic estimation error is within the secondoperational limit; and instructing the processing system to examine thesecond process when the second dynamic estimation error is not withinthe second operational limit.